Welderup google app like gboard from Aurora or fdroid
You can't get Google apps from Fdroid.
remove all permissions and connectivity, can I be confident that it is not still leaking my data?
Inter-process communication (IPC) exists, so you can't be completely confident. This is why a separate profile for Google/GSF-dependent apps is typically recommended.
Also, if I have an app like gboard used across multiple profiles will it some how link those profiles?
Profiles are isolated hence the recommendation of separate profiles. I doubt that any links could be formed across profiles.