[RPG] Does dealing 0 damage to a concentrating spellcaster require a saving throw

It Can (and possibly should) Be but we don't have an official rule

The rules do specifically call out damage of AOE or Multi-target effects to be roll once apply to all. However, it doesn't say the same about healing AOE or Multi-target spells.

With this absence of a rule specifically about healing you can fall back on how damage works and just assume that is how it should be handled and that has one big advantage, less time rolling dice. If your table doesn't care to much for rolling dice and wants to get back to the story you just roll once. Everyone adds it to their health. Then you get back to the action.

However you can also roll for each recipient or have each recipient roll themselves. This has one big advantage, more time rolling dice. this might be preferable if your table likes rolling dice, everyone has enough dice to do it at the same time, or you are using a RNG dice rollers. This also gives the players more of a hand in how much they get healed.

The case can also be made that individual rolls for heals will be less swingy in over all healing. It can suck to do an AOE 2d6 heal and roll snake eyes, thus giving everyone in the group 2 health when the average would be 7. Where rolling for each recipient would tend closer to the average, even if one of the group only gets 2 health back.

Ultimately it comes down to how your table and GM want to handle it. It would be difficult to determine what general practice is without a poll of some sort, and baring a direct statement from a designer or an errata added there is not going to be a more authoritative than a table level.

The closest thing I can see applying is that, as a player character, you can choose to take average hit points or roll for them every time you take a level.

Each time you gain a level, you gain 1 additional Hit Die. Roll that Hit Die, add your Constitution modifier to the roll, and add the total to your hit point maximum. Alternatively, you can use the fixed value shown in your class entry, which is the average result of the die roll (rounded up).

I'd make the case that it's always the PC's choice, since it's still the hit points of the PC we're talking about, and with RAW they can choose their HP generation method at any time they roll.

There's no rule that I've found that provides an exception that would allow the DM to dictate PC hit points, or any other character feature choices for that matter. So, unless someone else finds one, I interpret that as being the player's choice.

5E's 'exception based' design principle provides support for that. Crawford has said on record that if a spell or an ability doesn't explicitly define a feature or limitation, then don't infer it to be there. The example was: Fire Bolt says it sets unattended things on fire, so it does. Produce Flame doesn't say that, so you don't have to spend time figuring out if it does or it doesn't; it just doesn't. I would interpret that to mean: since there isn't something specific in the Wild Shape rules, don't infer anything beyond what players already do for their hit points.

Whether they always take average, or always roll, or roll once and keep that number for a given animal for the life of the character... that also seems like a good place for a character-driven decision that becomes part of their flavor, and I'd need something compelling to take that choice away.