No, it's not. Using Matomo on my own servers has nothing to do with the way GA etc. operates - it's an equivalent of going through my own Nginx logs and parsing them to generate diagrams and so on. Of course if I share personally identifiable data with a third party, it's a completely different thing - in this case it does not matter if it comes from Matomo or web server logs.

But I agree with your conclusion: what matters is how it's being used. In this case - whether you share/sell it to others or not.*

[*] But not only: it also matters if you take adequate care in protecting personally identifiable information or not.

In general, under the GDPR it doesn't matter much whether you process data yourself on your own server or contract that same task out to a third-party. Either that processing is legal or it isn't - ownership of the server doesn't play a role.

The problem with Google Analytics here is not that it's a third-party but that it's under US control.