There are no test frameworks in the mod, and every change introduces many regressions.

I am looking for suggestions on how to restructure the mod and which types of tests to introduce to cover the mod codebase with test cases and reduce the number of regressions.

This is an open discussion. I would greatly appreciate any help.

Just a suggestion, enable the 'Discussion' tab on this repository from the settings page. :)
This issue would fit well under there. Sadly i don't know how many check the Discussion tab, when it is there, as so few repositories makes good use of it. Perhabs this one can become an exception :)

minecraft has it's own framework called gametest where it lays out basically every test in one world and runs them in parallel

I will try the game test framework, and will at least try to find some info about it. Thanks!

if you want (even though your mod is fabric)
forge has some decent docs on it
I also was working on gametest for hexcasting
the key points are
setting the entrypoint
and the gametest class

and then throw structures in data/<modid>/gametest/structures
(and pass -Dfabric-api.gametest as launch args to get /test in game, reccomment creating a superflat world)