The Pro updates are not for Ubuntu based systems like Pop OS, and whilst some may actually work; as Pop OS isn't using Ubuntu kernels, others can create other problems that cause crashes, or could open worse security holes than the Pro update fixed, a flaw that won't exist on Ubuntu systems.
The Pro fixes will work with Ubuntu's official flavors though, but Ubuntu based systems are a different system (though this will be package specific; flavors installs can use different packages to what was installed on the targeted Ubuntu Desktop/Server system - ensure you read all security notices that are published for clear clues!)
Ubuntu Pro options should not be used with Ubuntu based system, unless you audit yourself what each patch does, and if it'll work or not work without creating issues. System 76 don't do this, thus they don't recommend using Pro or ESM (use Ubuntu if you want those).
Whether or not Ubuntu Pro benefits will be of benefit to you is a personal decision. Most fixes I've explored are for servers and my own desktop usage won't get much benefit. For those fixes that are desktop based - I've still not chosen to grab them, as I don't stick on the LTS release on many of my desktops anyway, thus ESM/Pro isn't an option open for me on some boxes. FYI: I am a Ubuntu member, thus have 50 tokens for Pro/ESM, so shortage of tokens isn't entering my own decision either.
Your usage will decide whether or not you get benefit as to the added security.
I personally don't see added stability though and aren't sure what you are referring to there. Most stability choices I see are made by us, and aren't related to ESM or Pro being enabled.
( I tend to not use releases once they EOSS (esp. on desktop systems); ESM sure makes sense to me there for those that do. ESM & Pro are more or less bundled in recent releases, but differences are release specific. )