As the title says, I recorded a run directly off my PS5 and uploaded it to YouTube, as the file size was too big to be exported to the mobile app for PS. My question is this:how to get an official time/timer for on screen? I only really have my PS5 and a cell phone, was curious if anyone had experience with this. Thank you for your time.

There isn't really a good way to do it. I wouldn't worry too much about it, adding a timer in after the fact doesn't really accomplish all that much anyway.

If the phone is a new enough model it should be updated enough to install PlayStation remote play and a speedrun timer.