i don't have much to say regarding most of your post since i don't find fault in it, but i do want to talk about some of the items you mentioned.
the pyro is a weird class in that i consider the character simultaneously very weak and surprisingly powerful. when the pyro is out of his element, he's about as helpless as a spy who's been caught out - moreso, even, considering the spy has cloak, misdirection, the option to equip the dead ringer for a completely free escape and primary weapons that don't have a range hardcap.
the degreaser/axt combo were certainly helpful to the pyro - the threat of an instant death from burst damage often played on people psychologically and would force caution and sometimes even outright stop people from moving into enclosed spaces - but i don't think they were the make-or-break items for the pyro, at least in pubs. moreover, i'd argue the pyro never needed the degreaser to perform well, and that you could do everything you needed to with the stock FT. i will say that the degreaser was - and still is, honestly - a straight upgrade to the stock FT, but it's habit-forming, which is why i would endorse anyone interested in playing the pyro to learn the basics of the class before jumping into more advanced techniques and unlock weapons.
that being said, the axtinguisher nerfs were completely undeserved and that valve hasn't simply reverted the ax to its old stats to this day annoys me greatly.
as for where the pyro shines, there's the obvious examples of denying ubers and reflecting projectiles, but i think people really overlooked the effects afterburn would have on people. in my experience, it would almost, without fail, make enemy players predictable to the point of them getting themselves caught in lose-lose situations. the most common experience is a pyro would light someone on fire, maybe hit them with a powerful attack like a shotgun blast or a critflare, and they'd immediately go for the nearest medpack due to afterburn. if you recognized that, you could intercept them and get a practically free kill assuming you don't make a bunch of mistakes once you reach them.
afterburn would also cause more delicate classes, such as lights and medics, to hang back after being ignited or even just straight up leave fights due to the desire to put extinguish oneself. heck, even just the idea of being ignited for afterburn would make certain classes hang back until you either died or had to retreat, therefore keeping them out of their prime range (anyone with a shotgun, sometimes soldiers, definitely less experienced spies)
there were also the instances where afterburn would actually get kills, but imo the best part of afterburn was always how it made people think. i think the afterburn changes from JI should be reverted honestly, as there isn't much threat of it now that a single particle doesn't ignite someone for the full duration any more. as a concession, though, i think spy should still deal with the current afterburn mechanics so one particle doesn't completely destroy any escape attempt he could try if he isn't using the dead ringer.
all the afterburn stuff aside, the pyro is also pretty great when it comes to groups due to how fire particles penetrate players. even if you didn't manage to kill anyone or survive, you'd often stall or outright nullify a push with a well-executed M1 roast, especially if the enemy team's medic is dead or not present.
this is all offset, of course, by the fact that the pyro's damage is stream instead of burst and how his primary is the only weapon in the game with a practical hard cap to its range, along with the lack of advanced mobility at a stock level. the class is easy to fight against if you know what you're doing, but a great pyro can make you question why you should suffer playing through the rest of the match. it's hard for me to really place the class on any sort of balance list, since the class has great upsides that are offset by extreme downsides and the ease through which he can be countered.
i didn't intend this post to become a rambling mess about afterburn and M1, but oh well lol
the ambassador change that was given is bad, but i think it could have used a change. i've never enjoyed playing against ambassador spies, since getting 2-tapped because they can click your head is a pain. i recognize and respect the skill, but that doesn't mean i have to enjoy the gameplay interaction (i say the same thing about the sniper class as a whole unless they're using silly weapons). i realize that isn't by itself enough to nerf a weapon, however i would argue that the issue is less with spies becoming pseudo-snipers or 2-tapping player from the front, and more in that the spy could position himself anywhere before sniping with the ambassador, which would result in a lot of obnoxious deaths.
although picking off wounded targets is part of the spy's class, what i disdain about the ambassador is that the spy can bring players down to that point himself. as such, a change i would have preferred to the ambassador is to make it so that targets above a certain health threshold will only receive minicrit damage, but once they get to 102 HP the gun will crit them. i feel like it'd solve the problem of spies playing sniper while also still retaining a long-range pick method for the spy, and play into his strength of being able to see enemy health to kill weakened players.
i won't argue on the demoknight stuff. i always thought he was fairly weak when someone with hitscan could aim was in the server, and so i thought the nerfs were utterly unnecessary. i also really dislike the change in concept of the persian persuader's upside. the caber is the most tragic loss of valve balancing for competitive players imo.
regarding the DDS, it actually really annoys me that the design hasn't just been reverted to its release stats, which was a simple +25hp boost. that would come in handy way more than you'd think for both snipers with rifles and huntsman snipers, but especially the latter if they had decent aim. now it's this sort of pyro counter item for some reason. i could understand afterburn immunity on its own, but the direct flame damage resistance doesn't make any sense to me. why punish a pyro for using their primary weapon if they manage to close the gap on a sniper?
maybe i've just been too absent from the tf scene, but it seems like people gave up on the jetpack really, really fast. it's too bad - as a big fan of flarejumping, the jetpack seemed like the Next Big Step for pyro mobility - and it still might be - but with no one experimenting with it heavily, we still don't know yet. if i still played the game, i know that thing (and the gas can, since i think it probably has a lot more use to it than people say as well) wouldn't leave my pyro loadouts. just wish it had the hadouken killtaunt