> the type of things Google could do with Gemini integrated into Google Docs

Google already does have this in Google Docs (and all their products)? You can ask it questions about the current doc, select a paragraph and ask click on "rewrite", things like that. Has helped me get over writer's block at least a couple of times. Similarly for making slides etc. (It requires the paid subscription if you want to use it from a personal account.)

https://support.google.com/docs/answer/13951448 shows some of it for Docs, and https://support.google.com/mail/answer/13447104 is the one for various Workspace products.