I don’t know if there exists such a thing as GrapheneOS account, but it is not required. You can add Google, Facebook or other accounts like with regular Android. I use a self hosted Nextcloud instance to synchronize contacts and calendar with DavX5 app. GrapheneOS has built-in apps. I use most of them. For the app stores I mostly use Fdroid and Aurora store for non open source software. I don’t use Google play store even sandboxed because I don’t accept the terms of use, mostly because they have the right to uninstall apps from your phone without consent or notice.
This functionality can be local. I use the Google keyboard with internet access blocked and it works. The only thing missing is the ability to search for emojis typing a word (they are still in the list) and some features that I never used and never understood why they are in a keyboard since it’s not related to typing text, like the gifs.
The only reason I see for a keyboard to need internet connection is to update the dictionary when it’s modified, but it shouldn’t prevent to work with an outdated dictionary.
When I searched for alternatives a few months ago, I couldn’t find anything satisfying.
In some countries, you need an ID to buy a sim card, so it’s linked to your identity, even if you pay cash.