Does GDPR (or similar) establish privacy rights to an employee’s use of a company-owned machine against snooping by their employer? Honest question, I hadn’t heard of that angle. Can employers not install EDR on company-owned machines for EU employees?

Yes, at least in the Netherlands it is generally accepted that employees can use your device personally, too.

Using a device owned by your company to access your personal GMail account does NOT void your legal right to privacy.

Yes. GDPR covers all handling of PII that a company does. And its sort of default deny, meaning that a company is not allowed to handle (process and/or store) your data UNLESS it has a reason that makes it legal. This is where it becomes more blurry: figuring out if the company has a valid reason. Some are simple, eg. if required by law => valid reason. GDPR does not care how the data got “in the hands of” the company; the same rules apply. Another important thing is the pricipals of GDPR. They sort of unline everything. One principal to consider here is that of data minimization. This basically means that IF you have a valid reason to handle an individuals PII, you must limit the data points you handle to exactly what you need and not more.

So - company proxy breaking TLS and logging everything? Well, the company has valid reason to handle some employee data obviously. But if I use my work laptop to access privat health records, then that is very much outside the scope of what my company is allowed handle.

Could the company fire me for doing private stuff on a work laptop? Yes probably. Does it matter in terms of GDPR? Nope.

They can, but the list of "if..." and "it depends..." is much longer and complicated, especially when getting to the part how the obtained information may be used