Google, unlike all their competitors, actually give Cloud API credits to all paying users of AI Pro and AI Ultra [1] - just use those for direct Gemini/Vertex API access instead of trying to hack the OAuth of Google's apps.
The problem with moonlighting a meaningful side project is that any marketing you do will alert HR to the fact you are moonlighting (HR in large corps pay to have employees' social media scanned).
In most cases you'll either be told to stop or in the worst case your employer will claim they own it.
[1] https://blog.google/innovation-and-ai/technology/developers-...