Pi SoCs have no sleep/suspend mode, so you'll be pocketing it powered on or waiting for it to boot every time you go to use it. Furthermore, you have to destroy a PSP to build this, AND buy an overpriced Pi (seriously, go look at the prices now) to shove in it, which will probably cost you more than a more capable and already-built modern retro portable.
All that aside, I have been down such paths enough times to know that this stuff is drawer filler within 3 evenings. People killing vintage hardware to build "cyberdecks" that are basically unusable and will just end up in the dump soon after is just the latest atrocity along the path to hell. Do what you will.
In that case, the Pi Zero 2 W ought to be enough, as its Cortex processor is leaps and bounds better, with a quad-core vs the Pi Zero's single-core, low IPC ARM CPU.
Crazy times we live in :)