In the Upwork example, screenshots are already encrypted and only accessible behind authenticated flows in their site/app; can be deleted manually (e.g. after you've been paid and don't need them for liability reasons); and automatically delete after some period of time otherwise (6mo or 1 year IIRC).

There are probably plenty of other time-tracking tools that give you more fine-tuned control over the privacy of your screenshots if you want that, but I can't imagine it's something most freelancers want to spend much time on.