There are people out there claiming that running or jumping or whatnot gets you XP in Athletics. It does not. I'm 6 hours in the game and got no XP.
I'm not sure what "cold blood" is, but no XP there either. Or annihilation. Or engineering. Something is amiss.

Engineering gets skilled from tech weapons and engineering checks on doors, fences, and mines.

Cold Blood gets experience when the Cold Blood perk activates. Yes, you have to take the cold blood perk before you gain cold blood xp.

Annihilation is doing damage with shotguns and heavy weapons.

Athletics supposedly gains experience from draining the stamina bar, but the only xp i've been able to get in it is from progression shards and forcing doors.

Just yesterday I got XP to Athletics after sprinting a few dozen meters, so it definitely works, but as for how, I really don't know.

swimming underwater gave me a some athletics xp (yes...i swam in the giant sewer river after i missed a turn with my bike on the highway)

Running, jumping and 'hurdling' around all have given me athletics XP, got some chasing cabs in one of the sidequests, but not sure how fast it does give XP as atm kb/m driving is so bad (for me) I'm running alot

I'm coming back a bit late after getting myself a PC strong enough to make the game run more comfortably. It seems the problem got away in the mean time. Although progress is extremely slow. After spending more than a hundred hours into the game and running around rather than fast traveling, most of the time, I managed get athletics to level 2… But the other skills seems to work correctly, now.
I suppose they shied away from admitting they had such a bug

I am not sure, only basing this on what I think is happening.

When I am running somewhere, I see the athletics XP popping up sometimes. Sometimes when I am parkouring over things. Sometimes when jumping. But bunny hopping doesn't seem to make it any faster.

I have noticed that I get it most frequently when I combine running, jumping and parkour. Or perhaps I only think that way.

But if true, then I think what happens is that there is some sort of counter. Every time this counter hits some value, you get the xp for your Athletics. Running gives it slowly or per stamina used, jumping gives some, but has a cooldown. Climbing gives some but has a cooldown. Therefore mixing all of those would give most to the pool that eventually gives you the xp.

But I am just guessing here. I haven't actually timed any of those so this is based on what I just feel is happening.

I gain in athletics periodically when i do double jumps and drain stamina. I also have gained it when i jump single/double off something and take damage from the fall.

Running, jumping, vaulting, etc. all give Athletics XP -- but at a glacial pace.

I made it a point to run everywhere in the badlands and it took about 20-30 minutes
for a single "+20XP" to pop.

It's a bit frustrating, because other skills are so easy to level (I'm looking at you, crafting).

any stamina draining works, even swinging melee weapons. I think I also got a lot of athletics when doing melee kills in slowmotion while sprinting :D but I haven't tried to repeat that.