This is going to be tricky. In go, the problem sites that I'm aware of seem to rely on user contributions, and aren't careful about checking the copyright status or licensing of contributions. In contrast, for chess it's the norm that problems are computer-generated from game records. But the nature of the game is very different: it's much easier in chess to create a reasonable quality of automatically generated problems with clear-cut solutions. (There's
https://neuralnetgoproblems.com/, but they're not exactly tsumego, a bit different in character.)
The classical problem sets are of course public domain by now, but the traditional solutions won't satisfy the average user's expectations on a modern problem site (choosing my words carefully as some people on this forum don't agree with those expectations...) And the majority of those problems are dan level, which is unlikely to be your core audience. So you'd need to put a fair bit of effort into checking the correctness of solutions, adding explanatory variations for wrong attempts, and estimating the difficulty level of each problem. And perhaps make easier problems out of followup positions. A lot of this effort should be automatable, but I don't think there's existing software which will just do all of it out of the box.
For kyu level problem books, you'll often see the same problem appearing in multiple books, which suggests that the position is actually public domain. If you could somehow get a large collection of books in machine-readable form and then search for repeated positions...
Honestly, I suspect your best option is to write your own web scraping code to put Sensei's Library problems into a suitable format. Remember that SL is Open Content licenced, so you need to acknowledge your sources. And remember that you can download a
snapshot, so you don't need to hit the server with thousands of requests.
If you go ahead with this, or find a better approach, please update here and let us know what you came up with!