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. And logging (storing) my health data without valid reason is not GDPR compliant.

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

Edit: Also, “automatic” or “implicit” consent is not valid. So the company cannot say something like “if you access private info on you work pc the you automatically content to $company handling your data”. All consent must be specific, explicit and retractable