"If you're using Cursor with a company (teams, enterprise) subscription, information of all your code commits is sent to their API."

Good. As much as we are all privacy freaks, if you are using company resources to do your own side projects, it is fair that the company should have visibility to it. Otherwise, get a separate personal subscription.

Note that you should not only have a separate subscription to things like cursor for non company work, you should also have a separate laptop/machine for doing anythng non company. One of the reasons why so many companies are cracking down on remote work is due to these types of violations in addition to other things.