The roles of pyro come down to: Denial, denying space with airblast, claiming space, causing and capitalizing off of chaos, as well as being a general menace to the enemy team's positioning.

Shotgun assists in passive denial as well as closer range single target focus; flaregun assists in longer range single target aggression and combo plays; detonator in mobility and multi target aggression; and jetpack in pre planned sacs. Each of these weapons synergizes with various components of a pyro's playstyle. It is also important to note that weapons such as the shotgun and flaregun serve more as the weapon, whilst detonator and jetpack are much more along the lines of tools to augment how you use your primary weapon.

A pyro should run the degreaser with either the shotgun or flaregun, and a pyro should run the stock with the detonator. Jetpack synergizes the best with the backburner due to the playstyle it promotes. Degreaser enhances your capability to use your secondaries, however if the secondary is more along the lines of a tool, running the degreaser is simply a straight downgrade. The scorch shot worked well with the degreaser due to it's fire and forget spam nature, while the detonator is much more methodical. For this reason, det spam will never be as viable as scorch spam, and thus the detonator should be used to realize it's movement potential. In this case, stock works much better due to the additional afterburn, which proves valuable when using the detonator to commit to engagements.

Success for any pyro player comes down to realizing their own playstyle and putting conscious thought into what secondary to use at any given time. The degreaser should not be blindly ran by a pyro, due to the limited value it provides to secondaries outside of hitscan options and the flare gun. Overuse of the degreaser to secondary spam ends up promoting poor mechanics and results in you finding yourself in more positions where you need the switch speed in the firstplace due to having the wrong weapon out at the wrong time.

Mobility greatly enhances pyro’s ability to fulfill all of his roles, so thus the mobility options of pyro provide a lot of value, and work rather well with more aggressive playstyles. The detonator is the typical choice for this role, however there exists a fine alternative to it, one that gives a higher potential to your plays at the cost of flexibility and frequency.

The jetpack provides great vertical mobility to the pyro, allowing for many unexplored routes and playstyles. The detonator is better for direct jumps and for aggression by itself, however the jetpack allows for the pyro to get into a much more advantageous position to flank and cause chaos from. The jetpack itself is less stealthy to initiate with, but allows for you to do much more indirect plays in the long run.

If pre planned (Ie recommitting from below on swiftwater second through the window, vigil first to curve around the backside of the flank, end of the round koth fights etc), the jetpack can lead to great returns. The sheer surprise factor of the long range mobility of a pyro with the jetpack in hand can exploit any errors in an enemy team's positioning, which there tends to be many of. The usage of jetpack forces your focus to shift onto the flamethrower itself, and fulfilling the roles of the pyro with it.

The height jetpack jumps lead to is what tends to result in it being denied if used to directly aggress, as it leads to you being rolled by hitscan. Integral to the use of the jetpack is the arc of your jump, which can take time to practice and get used to, but is a powerful tool in the hands of the right player. In addition, you can throw people off by doing a complete 180 of the direction of your jump midair; do spins after the first stage of the jump; or otherwise completely jump backwards from where you are facing. The key to the jetpack is to be unexpected and use it to put yourself into positions where you can flank and recommit. The detonator is always going to be better for jumping right at people due to giving you less height and time to be denied, but does not allow for you to get some of the position that the jetpack does. It is a case of specialization versus utility.

Technique is important, as it will greatly enhance your ability to do the correct jump at the correct time. Timing is everything, and the jetpack should only be run on lives you decide upon ahead of time. The weapon is a very poor play if you decide to just randomly run it and jump at players with no direction.

So then, a clear goal in mind, as well as the timing is what makes the weapon successful. The weapon itself is not at fault, instead it is the typical user of the weapon who fails to realize the full potential of it. In any case, it should always remain a niche choice for singular lives and plays.

this bit is mostly focused on casual

I find the backburner and powerjack to be most effective with the thermal thruster. The dragon's fury just results in you being an alternative soldier, and the degreaser has next to no synergy due to it focusing on enhancing your secondary (if you have trouble with switch speed, plan your jumps out better and start switching before you near the ground).

More specifically, the dragon's fury focuses more on single targets, and you're using the jetpack for mobility and getting behind, or directly landing behind targets that you dive bomb. Another downside not to be overlooked is the repressurization rate of the airblast, leaving you vulnerable and with a poor combat flow if you do have the need to reflect.

This leaves the phlog, stock, and backburner. The stock is great at doing most things, and if you plan on having fun by jumping around and reflecting things or airblasting people off ie on upward third, it's great. That being said, it doesn't have peak synergy with the set in my mind. You are not going to be using it to land in front of people the majority of the time; as to get value from thermal thruster jumps, you want a wide curve that swings around the target as other players approach from the front.

The phlog is simply not that effective unless you have a pocket for the set; you have no long distance secondary option to gain phlog with. This means you either directly jump into people with no airblast, or waddle around flanks to build phlog; and you might as well use the backburner in that case for guaranteed crits and some airblast

Onto the backburner. The backburner directly synergizes with both main reasons to use the thermal thruster and puts you in the perfect spot to capitalize off of said chaos. While you do lack the means to consistently airblast, by the same token it makes any airblasts you do use much more significant and trains you to be conservative with them. It adds quite a surprise factor and allows you to still do burst airblasting compared to the dragon's fury. In addition, the thermal thruster gives you a very good means to disengage from an unfavorable situation and get more ammo, or reposition to ambush again with confirmed criticals.

The powerjack allows for you to better surf damage, adding onto the increased knockback you take from having the thermal thruster as a loadout item. This combined with more base movement speed means for very rapid repositioning and the opportunity to surf around the map like crazy even without using a charge.

All of this results in a very flank centric playstyle that is constantly jumping into the air, one that is also frequently sent flying by things like projectiles, heavies, and sentry guns rather than outright dying. The sheer tempo of this loadout set can't be underrated, though versus competent heavies, sentries, and minisentries; you aren't going to find much luck on your own.

https://gtm.you1.cn/sharedfiles/filedetails/?id=2715869985

https://gtm.you1.cn/sharedfiles/filedetails/?id=2715815879
Specifically the pyro section of this, somewhat ties in.