Squeaking noise when brake pedal pressed, mostly at startup

Hi all! Long time reader here (all the advice is so very appreciated - esp. the maintenance videos. Someday I'm going to attempt that EGR cleanout...) and first time poster.

I've got a squeaking sound that seems to come from the brake pedal, occuring on startup on a 2013 Prius with just under 150k miles on the odometer. Here's a video, because a sound is worth a thousand words. It's a little worse/louder at the end of the video. Sorry for recording in the dark

The sound you hear in the video happens most often when pressing the brake pedal when first starting the car. It's been happening more frequently over the past few months. I've always occasionally heard it when driving if I press hard on the brake pedal at a red light or something. The sound seems to come from down near the pedal itself, and doesn't seem to change if the door is open (as it is in the beginning of the video) or closed.

Any ideas on what it might be? I'd appreciate any insight or educated guesses.

 

Thank you for the correct terms to search for! No wonder I wasn't finding anything by searching. I'm now reading through those threads, and might try a brake bleed. I'm a little worried over whether it bodes ill for the state of the brake actuator/booster...

Many thanks again for the very helpful information