I've been using HammerLib for quite a while and this is the first time I've encountered this. I used it in my build, then it stopped working. I launched a clean Minecraft with HammerLib because of this error and it still appears. If anything, I can provide additional information if possible.
P.S. I checked it on 1.19.2 and it works there
Link to logs:https://securelogger.net/files/b0785cbb-e35d-48e2-8405-7caf040936ff.tar.gz
Screenshot of the error:

Thats caused by mod itself, trying to determine, whether its genuine. You can try recompiling it from source, from 1.19.2 branch, removing said code

Thank you, but how do I do this?

On GitHub itself on the repo page choose the desired version, download source code, go to the ModSourceAdapter.java, find in there piece in charge of mod authenticity check (getModSource method) and make it not be using network API (whether making it not making requests or disabling said check at all), cause that's where problem in itself lies.
It also was mentioned in another issue, but trying those network requests in the main thread ain't the best practice.

Thank you