This seems to be the shape move to help the left side. I'm too sad to do any deep reading right now. He still has to be a little careful, so I'm betting on something like 12-8 next.

In case I'm wrong I should be explicit about what I think is going on at this stage.
I think I've captured two stones in a snapback and connected through while black has a slightly ill looking group on the left that should be fine and a group on the right which has an eye and two halves.
My group doesn't actually have an eye from that capture but should have enough going for it to live without too much discomfort.
I realised since last move that black has that second half eye at 15-4 so is alive unless something funny happens.

I don't really understand why black's last move didn't ladder at 9-5.
Saving this stone feels like it banks a few more forcing moves by keeping this group unsettled?

If b7-5 then I play 12-8

If black got to link up over the top here and I had to play a low value move inside that would feel bad. This might make 11-2 my sente too

Only an emoji:

No idea why he would make that exchange of 8-5 for 7-5. I considered atari over top first, seems like bad timing. I really wish I could continue the attack. I also don't want to die or get surrounded with my wall by accident. Gonna chill, think about the shape, get my work done, probably reread the moves and play another move in a couple days.

Knight's move approach.

It's been a while! I forgot just how much mess I was in here - actually, maybe a little less than I was thinking back then. I don't think that my lower right group can realistically be threatened too much- I can make a second eye at 15-4, which I'd forgotten about. It's still quite bad, but definitely can be made up with a fight, and likely can be made up without a fight and just proper judgement. Here goes!

I considered adding another move to either the left middle or right middle groups of mine, but everything is already nearly alive on the right (so play away from thickness demands that I play away). The left middle actually had quite nice shape - I can't see a way to cut it, and it's very much out in the center. Still, the slide is a big followup locally. Also a candidate is playing in the top right corner, but I want to have as many interesting areas of the game as possible to catch up, so I don't want to trade enclosures and make everything strong.

Looking over my comments I agree with almost everything I said - except that I needed to see his tactic here. I even mentioned it in my post for the response to the kick, which was the correct time to read out the sequence - but I failed to read out the sequence! In retrospect, I should have just gone for the good shape move, wand in general I should go for more good shape moves.
Speaking of good shape, I have tried out the bottom left large knight's move a few times during our break, and analyzed them with Lizzie. Since we're so far away from the original, and I never played a similar shape to this game, I figured it would be okay. Actually the first time I tried this large knight's thingy I forced a 6d to resign in 55 moves on WBaduk - everything went just as I planned it to go in this game
I think I'm 3-1 overall playing the large knight's move fuseki-thing so I definitely recommend trying it out, if you want to skip over the territory meta that's popular these days.

I expect him to back off small knight's as normal, which is one line away from the ladder potential in the center. Then I think I'm going to play 4-2 immediately in the bottom left. My plan is to try to stave off his attack on my approach stone by having a strong group already in the center. Maybe with some counterattack on a good day I'll be able to take the upper right a little extra efficiently.

This game looks just slightly alien again now. Like that feeling when you look at someone elses game and it's hard to put yourself in their perspective right away.
I think I had a bit of reading done for some peeps and weaknesses and things on the bottom side previously so I might need to refresh that.
For this move, I was very tempted to play high at 4(d)-14 but decided that low should be fine. I'm mindful that black has a little bit of centre influence (though I wouldn't say thickness) from the lower side stuff. If I play low then I feel like at some point a shoulder hit might become sensible but if I played high then something like 3(c)-12 might become effective and annoying soon and I might be inviting complications. I'm not dissatisfied with the game so far so simplicity feels good.

Knight's move.
Slide.

In the games I've played with the large knight's move before, attaching at 4-3 is often recommended by the AI. But this isn't that position, and I think that 4-3 attach is a mistake. I currently have a good shape with 6-3, 7-5, 7-6, 8-5. But whenever he plays an attach on top at 6-4, I will have to connect at 7-4; there's some aji there. So against 4-3 attach, 3-3 hane, 3-2 counterhane, 5-3 atari, 4-2 connect, 6-4 pokes at my cut in good timing. I'd like to atari underneath (5-2) before connecting but I think his immediately cutting (7-4) will be too strong.
So instead when I slide, if he pushes me down I can connect everything. His cut at 7-3 does come with atari, but even so cannot connect back to his group.

So locally I think the slide is good shape, but that doesn't mean it's the best move on the board. I suspect that assisting my stone at the top left is a little more pressing, AI probably won't like this move much. I really don't want to have to worry too much about this center group though, and I want him to have to worry a little about his bottom left group. Of course he can play a ladder breaker on the side to assist it, but I think I'll have followups to reduce and take influence. The ladder I'm talking about, by the way, is cutting at 8-7, double atari at 8-6, and ladder leftwards at 8-8. Mike's last move is just one line too high to break this - if he had played the large knight's back-off then I would have felt quite gloomy right now

Perhaps 5-17 kick is on the agenda for him. I think the one move he probably shouldn't play is 3-3, because it reduces the effectiveness of his ladder breaker on the side when all of his groups are already solid.

Had a dip in concentration here and thought this was a slide in the top left corner. In that case I wanted to play for the outside (8(h)-17) and trying to read that ladder gave me headaches (I'm confident it's one of those that looks as if it's going to work for white but then black just connects up to the wall.)

For the actual move played (bottom left) my 3-3 response might be slow, but neither my two stones or his outside formation quite have 2 eyes yet so something around here seems fine and taking the side (perhaps 3(c)-9) seems uninteresting since black could keep me low. Black probably doesn't need another move but I think maybe leaves behind some funny shape on the bottom

If W 3-17 [c17], B 3-18 [c18].

Attach underneath.
If hane, then counterhane.

I'm very satisfied with the slide exchange. It was unlikely I'd be strong enough outside to ever play 3-3, so it's basically pure positive for me. It's true that he's going to have a large lead on territory, but that doesn't mean that it's immutable. If he gives me good exchanges like this for the rest of the game I might just calmly win by 10 points. I'm quite good at playing against large leads in territory, at least when I can see the board.

Anyway, now I get to go here first, too. This move is definitely better than the slide, because against the slide he can play on the right with a ladder breaker and comfortably tenuki to the upper right. This way his ladder breaker's value is going to be diminished - it's going to look just a tad overconcentrated. But mostly I'm just playing a normal move, giving maximum strength to the weakest group.

If b 4(d)-18 then w 5(e)-16

There are a few choices here but in the absence of particularly interesting stuff going on this pattern seems reasonable

Connect, he connects, then I connect.
We're playing out joseki. He gave me the chance to take the corner. It would have been silly for me to take him up on his offer. Now, he chooses whether to play 6-16, pressing down, or 2-17, taking territory, or tenuki. None look great for him so I'm making plans after he makes his choice. All I know is that I'm almost certainly pushing up at 6-16 if he plays 2-17.

I don't think I have great prospects to develop if I push at 6(f)-16 so I won't make black stronger

Push.

I got burned really badly by a 3 dan a few months ago when I tenuki'd this group. It needs another move. The question is only between extending up and jumping to the side. In a game where I'm behind and I'm pointing towards a 4-4, pushing is really the only way to play.

Now it's up to him to finish the opening. I'm guessing he plays 17-14, low approach. But who knows?