I see it's been recommended you don't drive. You sound like you know your way around a wrench, so make the call.
Sound from videos are very difficult to use for making any determination. The wind sound from the fan or what ever, makes one of the video's sound like the engine is going to blow up. Your first one is best IMHO. In that one, it's really not that bad. But you are hearing something has changed or you'd not be hear.
I don't recall you stating any performance issues or low oil pressure.
As noted earlier, your plugs looked good but a tiny little bit of carbon build up. But (picture) didn't show any indication of issue with combustion chamber (rings or valves) IMHO. The tiny carbon build up is one more clue of minor combustion issue, which weak coil, spark plugs and/or dirty injector could be culprit. Injector get loud, if one's not making noise it's not operating.
At one point you removed the S-belt and noise stop for a moment, I assume on start up. Could this be a momentary stuck fuel injector?
I purchase about 4 tanks of gas from my King Scoopers, I'll not do that again. It cost me much more in 44k to clean out the gunk, fuel filter and time than I saved in gas $$. High test Shell or Conoco is about I'll buy in my area anymore.
I think your weekend plans a is good one. But I'd do it a little different, and have some fun ,,,Foot ball... Go Bronco's.
Here's what I'd do: Check each fuel injector as discussed. Assuming you suspect one or more. Then add some 44K or equivalent cleaner, to 1/2 a tank of high quality 91oct gas. Run until cleaning agent get into system, the let rest (soak). Then take a HWY drive (1/4 tank) to some great spot, let engine cool down a bit while having lunch or watching ,,,,FOOT BALL....GO BRONCO'S..sorry. Then drive home, let rest ~hour and recheck fuel injectors. If sounds is a little better, have fuel injectors cleaned. Just make sure you find a good shop to do it. If you do the on vehicle injector cleaning you'll also get fuel pressure test in the deal. Off vehicle you'll get condition & flow tested. Follow up with one more can of 44K in full tank of high test.
If not happy then move to next step. But get a second opinion form a mechanic that works on Toyota high millage 2UZ-fe regularly. He may say sounds is normal.