It depends on the SU.
Basically, SUs in a Corps HQ have a chance to support any battle for that Corps. SUs in a Division or lower always support that unit - you’ll see their CV go up as you attach them.
Armies usually aren’t close enough to the front to lend support...but having the widest command radius and being the first ones that can really reinforce a beachhead or pull from/send to virtually anywhere, are often a good place to keep construction units and assemble support until you need to assign it.
To that point, the rule of thumb is you stick artillery with a Corps, direct combat stuff like tank or ost battalions in the units. The Americans in particular should have virtually every every unit maxed out with attached tanks, engineers, SP arty, etc. while their Corps have six artillery battalions. The CW are still SU rich, but slightly less so - and their Corps can’t send as much artillery support as the Americans - but some of their SUs, like the Assault Engineers, can turn a unit into a powerhouse. The axis have a weird mix of not having that many SUs comparatively, quite a few being little more than fodder, and then hidden things like Tiger Battalions that only add a point or two of CV, but massively affect the actual combat they fight in.