Streets Of Rage 4 is good because it uses in game time (so you don't need to worry about streaming via OBS / Livesplit etc - just hit "Share", "Broadcast" and away you go).

The Last Of Us 1 & 2 are also pretty popular speedruns on PS4.

Here’s a list of all PS4 games on the site, sorted starting with most popular.

https://www.speedrun.com/games#platform=PS4

if your good at platformers crash bandicoot

Detroit: Become Human

Bit late to this, but uncharted has a timer of it's own

Section 1 of FAQs https://www.speedrun.com/speedrunning/thread/pt010