What attributes of a Pokemon can be improved?

The only things that cannot be changed are:

• Any specific IVs that aren't 31, such as wanting 0 speed for Trick Room
• Any moves that are exclusive to special events (which SwSh does not have yet)
• The gender of the pokémon, if relevant to the species
• The pokéball it is stored in
• Anything that relies on the PID (Spinda spots, whether Wurmple evolves into Silcoon or Cascoon, etc.)
• Pure flavour information such as characteristic ("proud of its power", etc), time/location met, real world location (used for vivillon formes), shininess

Everything else can be modified.

• IVs can be maximized to 31 through bottle caps and hyper training (requires level 100)
• Natures can be changed through the new mints
• The ability capsule can change an ability from "slot 1" to "slot 2" and vice versa
• Egg moves can now be transferred to pokemon of the same species through the daycare
• EVs can be reduced by EV reducing berries or reset entirely by an NPC on the Isle of Armor and retrained in the desired stats
• The Isle of Armor DLC includes a way to give or take away from a specific pokemon the ability to Gigantamax
• The Crown Tundra DLC includes a way to give a Pokémon its Hidden Ability (although it cannot revert a Hidden Ability back to a regular one)

It can also be assumed that any Pokémon that could only obtain a certain move in a previous game through a move tutor or something won't be able to pass it across once Home is out, but I'm listing that separately since it's unconfirmed.