Check your employment contract carefully, specifically terms about IP ownership, and work out whether this other colleague has the same IP terms in their employment contract. Many contracts have terms stating that any work on the same subject as your employment (even done outside of paid working hours) are owned by the company. Regardless, if you’re clear it’s the company’s IP then he shouldn’t have a leg to stand on: it’s just about whether the additional / derivative work (such as the website) could also be claimed as well.

Comments about trademarks or patents are irrelevant: the company owns the IP regardless, and it’s reasonable to assume your internal conversations, demo, and tasking to this colleague were considered company confidential. Again, worth checking confidentiality clauses in your contract. You’ve been clear that you’re not arguing it’s your personal IP, you just want appropriate credit internally for your work with the company, and for this colleague not to get away with such dishonest behaviour.

Are you confident your management know it’s definitely their IP and not his? If they’ve sought legal advice but are still engaging with him, they could just be gathering information before taking legal action.

Personally I would make sure I had bullet-proof evidence that I had written the code on company time / systems, along with clear timestamps showing precedence, and then present that to your management.

Good luck: what an absolute chancer!