Ideally the new update should be focused entirely around competitive play with not only bringing in the much-needed redo of the comp MM ranking system, but also focus on esport themed war paints and whatnot. I doubt valve will fund a major for TF2, so I won't ask for something so unlikely to occur.
I'd love to see smaller hitboxes on all pyro weapons in exchange for range. Make it a more rewarding weapon to use. I like the pyro changes but it needs tweaking to make him more viable across more encounters, but take more skill to use. Tweaking heavy would also be nice. The movement melee nerfs were well warranted but I would like to see more dexterity with his minigun (entirely removing rampup as well as buffing movement speed when revved) in exchange for a smaller health pool. I would at least assume that would lead to the 2 most unfun classes to fight and fight against in this game to be fun for once.
As said above if there is anyway to optimize this game with the apparently shitty build of source that it was created on, please do so. A modern PC shouldn't be getting frame-raped by a 10 year old game at any graphics settings. Maybe some more UI tweaks and some HUD changes will go a long way as well.
All of these together doesn't fix the main issue with comp participation though. Unlike in many esport titles TF2 does not have a good bridge between casual play and competitive play, and if you want a healthy long-lasting community (rather than just leaving said community to its own crafty devices) than creating said bridge is paramount.