Can we get some context on udyr buffs ? It is a very weird one since damage wise it seem like nothing had changed ,You gain 35 dmg on the proc at lvl 18 and lose 50 dmg from the aoe burn , and early on you lose 10 aoe dmg for 15 proc dmg , It' a really weird buff or nerf that i cant understand

It's primarily meant to be a small early clear buff and make the Phoniex Cone feel like an impactful proc again. The problem is since you can actually get more than one Phoniex proc out of each cast in the jungle so any damage boost there double-dips hence trimming a bit off the AoE. This is because you can Phoniex Cone, AA,AA, Phoniex Cone.(Recast Phoniex), Phoniex Cone, etc. Later with CDR in the jungle you're generally overlapping the Phoniex capes if you just spam the button and wasting the end of the proc anyways.
In team fights the damage change gets a bit messy. On one hand it's much more difficult to pull off multiple procs on the same target with the same cast (generally not even worth attempting - swap to another stance between ), on the other the liklihood you stick to an enemy for the full 5 seconds isn't high, and if you only stick on them for 1-4 seconds the damage is just strictly higher.
In short, it's a noticeable buff to his early clear and in most cases will be a damage increase overall (though a smaller one late game)