I've got a couple of family members that are still happy with their respective 2013 MacBook Air and 2013 Macbook Pro after adding a larger hard drives, updating to Big Sur, and installing fresh batteries for them a couple of years ago. Problem on my end is I can't reasonably recommend/keep them in service at this point because Apple shut down support for Big Sur and the update software doesn't want to pull any of the current iOS upgrade versions because Apple delisted the 2013 models.

I've seen a few articles referencing the use of patches to essentially trick the current iOS into installing but I'm not sure how much faith I can put in those to not have their own vulnerability or built in spyware. If the experts her in Urban Commandos can share their perspective and experience, I would sure appreciate the advice.

Should I retire the still very functional hardware or do you all have a path to iOS upgrades to send me on?

10 years old, retire them, you might be able to get a trade-in credit from Apple.

Apple provides software updates for hardware 5 to 7 years after the date of discontinuation.

Meaning those models will only update to Big Sur. But will get all the updates for Bug sur.
They will no go past Big Sur, so what you are calling support is actually versions newer then Big Sur and/or security updates.
IF a major security issue comes along Apple may still provide an update for older versions of Mac OS but Big Sur would be likely the oldest supported version.

As long as the "Patch" you are referring to is the one that I think you are (can't remember the name) all it does is change a listing in a config file so you should be OK there BUT keep in mind, that hardware was never tested for whatever version of MacOS you put on it past Big Sur and performance may not be what you think it should be.
Also, Apple will not provide phone support for those models past Big Sur, so you become your own help desk.

it could run fine, no problems.
it could run slower but usable
it could run unbearably slow
it could fry your battery in a puff of light grey smoke.

No body knows until you try it.. so report back and let us know.