I would just give the projectiles a random fake height when spawned and the cover objects and whatever else a value for their max height and allow them to go through when they exceed that. It's simple and it will work consistently for all objects in the scene. The height variation can always be in the 0-player height range.

ideally, some bullets would collde with the barrel, and some would not. Another part of the problem is what if there is another object in between that a projectile has to pass over.

the traditional way to handle this is objects provide a percentage of cover.

"all barrels provide 50% cover".

so each attack has a 50% chance to hit the barrel, instead of traveling on to the target.

so you do a raycast from shooter to target, checking for intervening cover. when you hit intervening cover, you do your percentage check. if the check fails, the shot hit the cover. draw some bullet holes, play a sound effect - next bullet. if it makes it all the way to the target, then your resolve the attack (projectile hit).

you can also do stuff like "all barrels provide 50% cover, 90% if the target is crouching."

What happens when you just shoot a bullet at the barrel and there's no-one behind it? Will it hit the barrel 50% of the time?

I think it needs to be consistent, making it so, if there's a figure crouched behind a barrel, bullets now hit the barrel 90% of the time doesn't seem like valid gameplay to me.

Whatever you choose, try and make it consistent, whether a player is taking cover behind the object or not.

What happens when you just shoot a bullet at the barrel and there's no-one behind it? Will it hit the barrel 50% of the time?

top down 2d - remember? no different than a turn based tabletop wargame as far as combat rules goes - such as squad leader. whether the dev wants to draw some bullet holes and dust clouds as eye candy when the player shoots at barrels is up to them. for the typical "max gameplay effect" most devs opt for, you'd draw the eye candy every time. which of course means you need to move the bullet full distance first to see what it hits if anything (player, wall etc), then move back to the barrel if it can't hit something more interesting.

a simpler trick would be just do traditional stepped movement with collision checks as usual, and if you hit a barrel and fail the "dice roll", it draws the eye candy, else it travels on to the next obstacle. if that's the player and they are crouched, reduce chance to hit about 50%, as the size target they present is about 1/2 of non-crouched. that way you don't have to worry about proximity of barrels and players. the two basic mechanics (IE game rules) of "barrels stop 50% of all bullets" and "crouching makes 50% of bullets miss" combine to give you the dynamic of "crouched player behind barrel has 75% cover".

the next step past that is multiple elevations (ground, slope, hilltop), and basic 3D LOS/LOF calculations as seen in panzer leader and panzer blitz by avalon hill.