Just to clarify further the limitations are two tiered.
The first is by Google service, the second is by account.
At any given time you may have up to 50 refresh tokens across any Google services for a single Google account. Up to 25 of those can be used for an integration with Google Analytics.
These limits are not based on the applications that you decide to integrate with in any manner. They are put into place by the team that simply runs Google’s OAuth2 service.
So let’s take two examples.
First is the easiest one, if you integrate with 26 sites, upon authentication of the 26th one the first one will be deauthenticated. Because you have exceeded that the number of refresh tokens that a single Google account may have that integrates with analytics (in any capacity), they will revoke the first one to keep you under the 25 analytics per Google account limit.
A second one is let’s say you decide to authenticate 25 sites into Google Analytics. Then you decide to authenticate 20 times into a service that uses Google drive API. Then you decide to authenticate six times into a service that uses YouTube’s API. In this case on the sixth authorization for YouTube, the refresh token for the first Google Analytics account will be revoked even though you are under the 25 limit, because the 6th YouTube authorization puts you over the 50 refresh token per Google account limit and therefore they will revoke the first one regardless of the service it belongs to to keep you under the limit for the entire account.
Again as you’ll notice none of these are affected by which app you use for Google Analytics or YouTube or Google drive. They are account limits that Google puts on the account, not based on the actual integrations you use.