Programming

If you implement it from fresh then it is a new program. What matters is what your contract says about what you produce - some contracts pay claim to anything you make even outside of working hours.

Also if you rewrite it, while technically it is a fresh project if there are substantial similarities in how you implement it there could be an argument made that you have reused code that belongs to the company. Even if that is technical false it could be something you'd have to defend sometime in the future. As others have said, implementing the program in a different language and using a different methodology wherever possible should help protect against that.

I think the advice others have given that you should review your contract with a lawyer is sound even if this will be FOSS. It's mainly about ensuring you don't inadvertently open yourself to potential legal repercussions down the line, even if your employers at the moment seem benign. If you do work for a company that lays claim to everything you produce even in your off hours then I would strongly recommend you consider leaving or an exit plan, particularly if you are the sort of person who would be working on your own projects for fun or even your own business ventures.

Write it down for now so you do not lose the memory if it is so precious to you. Maybe it will be even better the next time coding it. I think many coders have a "loose copy" or a "code gist" of previous versions of their favorites codes around. I never created a code that I framed and hanged on my wall, but some came close. I would not publish it under your real name any time soon. At least not as long as you work in that company +1-2y. If you choose to publish it in the next 6 month under a very different name, in another account, with another repo name, because you love FOSS so much, and it looks different to the original code in format and style (and the presentation of data = frontend), then I see no problem. Just two guys having a similar idea. Not a lawyer though.

Walter Bright had a lot of back and forth over the Digital Mars C compiler and Symantec.

Richard Stallman would encourage you to publish it.

Without a non-compete clause, I imagine if you changed it enough you'd be alright.

I personally know someone that has started essentially the same company multiple times, and just keeps selling the companies off. It's different software each time, but it does essentially the same thing.

Ask your boss.

Right now there are huge financial interests in the tech sector arguing that anything output from a chat bot is non-copyright protected and non-infringing on the copyright of the training data. So use one of them to get something close to a working idea of the program and then edit that to create your self owned copyright of your program.

I assume you weren't a contractor, but if you were it depends on whether your contract specifies "work for hire."