Is there a learning curve for tanking *alliance* raids?

[Jeeqbit]

there's this mental block where I stop at alliance content, and feel I must step back and either heal or DPS.

Remove the mental block. There's absolutely nothing different about it. Just run in with tank stance, pull, use rampart when there is a tank buster, pickup adds.

The only thing different is adds/bosses are often split into sets of 3.

Set A is on the left.
Set B is in the middle.
Set C is on the right.

So check in the party list which alliance you are. If you are A, go left, if you are B go middle, if you are C go right. And pickup the boss or add at that location.

Often, the adds will tether to eachother if too close, so keep them separate (at left, middle or right) unless you know that they don't tether. Tethers are bad because they empower eachother and make themselves invulnerable or hit too hard to be tanked.

That is literally all you need to know.

Maybe it's the WoW programming of past years, but I feel the weight of "being responsible for" that many highly experienced people's enjoyment of the content

There are 3 tanks. It's usually not a wipe if 1 tank dies, although rarely I suppose it could be if there is a tethered add situation.

and assume that with so many tanks on the field that these fights must have more complex elements

Nope. Just do it.