Richard Stallman would encourage you to publish it.

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.

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."

Ask your boss.

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.