How is it different from Puter AI, which offers auth + free inference?
(And yes, I hate their name too. I don't honestly know how defendable an entire technology term actually is. It also results in terrible Googling.)
I would also build this on top of firebase marketplace: https://extensions.dev
I know that might sound like putting the server back to serverless. But I would say it's being your own serverless provider - once you have the platform installed on your servers you can build frontend-only AI apps on top.
Hope you don't mind the self-plug. Your approach definitely a ton of advantages when starting out (no infra to manage etc).
One challenge on frontend-only apps is if the prompt is proprietary then this will be exposed unless you will then offer prompt templating or prompt mapping on your side i.e. the frontend says prompt: Template_123 and then this maps to the actual prompt somehow. Prompting is important still and maybe for a while so having the internals externally available could be sensitive.
(I suppose, relately, I have trouble understanding why anyone would just sort of presume OpenAI would be forever the best backend here as well?)