I was reading Can an employer perform deep packet inspection under the GDPR?, where the OP is asking whether GDPR protects them from their employer running deep packet inspection. I would have expected that the GDPR wouldn't be in any way relevant, so I am asking a broader question: if I am using a work computer, something that belongs to my employer, and as is usually the case, anything on that computer belongs to the employer and not me, in that case, can the GDPR protect any of my data?
My thinking here is that the machine and the network I am using both belong to the employer. Under the assumption that they require me to only use the machine for work-related activities and I am therefore under no obligation to have my own personal information there, how can I claim any kind of GDPR protection? This isn't a case of a company harvesting data from its clients or prospects but of an entity processing data that actually belong to it anyway.
Is my understanding wrong? Can the GDPR be used to argue that an employer cannot look at some activity (any activity) I am performing using their infrastructure?