No it's not. Monitoring the DOM is not a violation of the GDPR. Why do people make this shit up? This would be like saying that a site does not have access to the form data input by its users. Do you think sites are 100% fully end to end encrypted and the backend has no visibility in the messages being posted?
Fuck, this would be like saying that all userscripts and browser addons are in violation of the GDPR because they can tamper with user data.
Also hilariously enough the GDPR is a joke. I work for a cybersecurity company that has customers in Europe and our EPP software exfiltrates massive amounts of telemetry without the end user even being aware that our software is running. Said software is constantly scanning all of memory and could collect whatever personal information it wanted to (but we don't do this) to be sent up to our servers. This is also literally what any video game's anticheat can do and I've never seen a single GDPR warning for any game with anticheat.
You guys do understand there is zero privacy right?