As an old programmer (old being the operant term), I think it might be possible; but I have no experience with the PC platform. I wish it were an option in the OS and would update a box in the lower right corner of my screen where the 'notifications' box currently lives. In my age-affected mind, the timer would start when the enter key is pressed and would stop and display when a new screen is displayed. Of course, it would have to be based on each open tab and not be affected by changing tabs, ie, the timer would not be invoked when changing tabs.
Many decades ago I ran a multi-state private data network; there were no public ones in those days. It was driven by IBM hardware, AT&T modems, and CICS on the mainframe. We didn't have tools robust enough at the time, but I always wanted to put a response time counter on the screen when it was refreshed; so that we could track and confirm what users were reporting as slow response so that we could troubleshoot and resolve issues.
