There are a couple alternatives, but they either require you to manually extract cookies from your browser's dev tools and copy them into the extensions settings, or they don't stream responses (meaning you have to wait awhile before you hear back).
I'm planning on putting up a blog post describing how I went about building this, but the hardest parts were reverse-engineering the API and figuring out how to get browser-based authentication working in the extension (since OpenAI put ChatGPT behind Cloudflare, which blocks programmatic auth requests).
I haven't pushed up the code to a hosted repo, but if anyone's interested in me open sourcing the code (or contributing), I can be found in the project's discord: (linked in the extension's README).