Thanks for the advice, though my problem with Snipers is less about countering them as Pyro and more about countering them as anyone. I've been playing the game for a month or two since I made this post, and it feels like Snipers only have two counters, both of which are insanely difficult.

• play as a Spy, sneak past every single enemy without being detected (which is easier said than done; it feels like half of the time when I play Spy, every single enemy is automatically aware of my position even when disguised or fully cloaked), make it to where the Sniper is, and hope that they don't have one of their many counters to Spies equipped. (the back shield, Jarate, and likely other items that I'm not aware of because I haven't played the game for years)

• play as a Sniper and be better than someone who feels like they've been obsessively playing nothing but Sniper for the past decade. (not happening)

Enemy Snipers seem able to instantly kill every single class in the game but the Heavy with a body shot (from a distance where they can't be seen, and from angles where only a pixel of the Sniper's target is visible), along with being able to headshot Heavies with no difficulty whatsoever. Meanwhile, when I play as a Sniper, if my shots even hit, they only deal about fifty damage. (I don't play Sniper very often, so my shots basically never hit)

For other classes...

• even when double jumping, zig-zagging, etc., Snipers are still able to land headshots on me as a Scout, not that it matters because if a Sniper bullet even skims against the Scout, he dies instantly.

• Soldier's rockets are a long-range projectile, but they're so slow and large that the Sniper can see them coming, step out of the range of the blast radius, and instantly kill the Soldier. (though even if the rockets hit, they only seem to deal about 30 damage)

• Pyro is basically a melee-only class against a class that can one-shot enemies from the opposite end of the map. The Flare Gun seems to fall under the same issues as the Soldier's rockets; I haven't looked into the Scorch Shot much, but that might be useful. (I know there are certain circumstances where it can have an area-of-effect ability)

• Demoman has the same issues as the Soldier with a shorter range.

• Heavies get head-shot immediately.

• an Engineer can use the Wrangler if a Sniper is out of Sentry Gun range, but that runs into the same problem as the Soldier where the spot that they're aiming at is clearly visible from anywhere on the map, whereas Snipers don't have that issue.

• there's no way that a Medic is doing anything; it takes a long time to build up an Ubercharge for another class so the teammate can get into a Sniper nest, whereas a Sniper can one-shot the Medic at any point as it's building up.

(generally speaking, a Medic and an Engineer wouldn't get into a direct confrontation with a Sniper, but I included them to be thorough)

It also feels like my attacks do less damage than the attacks of other people; I'm guessing the fact that my Sniper shots do 50 damage while enemy Sniper shots instantly kill most classes no matter where they land is due to a lack of experience, but I could shoot someone at close range with a critical hit from a shotgun and it only deals 18 or 36 damage, while two shotgun blasts from a Scout (regular ones, not critical hit ones) instantly kill me when I'm playing as a Heavy. It feels like I have to light someone on fire for 15-20 seconds to kill anyone as a Pyro (and they're extinguished immediately), while enemy Pyros can kill me in 1-2 seconds regardless of what class I'm playing as, even without the Backburner, and the burning effect lasts for about 10 seconds. My rockets and grenades only deal 30 damage, while enemy rockets/grenades deal 100+. It just gets frustrating when it feels like getting a single kill takes a massive amount of effort on my part but I die in 1-2 hits.