Other answers have fairly well covered the copyright on the code. In short, you can continue to distribute it under the same GPL license. A related but separate issue is trademark on the name. You said it's rebranded, so that's probably pretty well covered. Just be mindful of how you mention the old name. You can say it was forked from Acme, but don't want to imply it's endorsed by the old maker, by the maintainers of Acme.
Regarding the tools the original author used - there are two copyright issues around AI / LLMs. The US copyright office issued some guidance about this in January 2025. A summary of that guidance:
The person has copy rights only to their own work.
If the person who originally published the code wrote the code the way they wanted it and used AI tools for syntax checking, perhaps boilerplate code, etc, but they actually wrote the code while using AI-powered tools, they have the copyright the same as of they used a pencil, and licensed that copyright to you. No problem in that case. This would be if they designed how the code should work.
If the person entered a general description of what the code should do and the AI wrote the code, and then the human fixed errors in the AI, it's probably not copyrightable.
If the person requested a program that does the thing and the AI handed them someone else's code, the person who actually wrote it has the copyright. There is a lot of controversy around that, people worried that is happening. I've been unable to make this happen, despite consulting with some AI experts and them helping me try to make an AI regurgitate and summarize sentences from the source material.