If I were the DM I would just rule that monster abilities that resemble spells are spells. Would involve some adjudication but seems workable. Have you discussed this?

I've got an Oath of the Ancients paladin in my group. I play it as if the thing behaves like a spell, we treat it as a spell for the purposes of this feature.

Hey! I feel you a lot here, I have an ancients paladin that's up to level 18 at this stage, and it's only pretty recently with a shift in adversary type (fighting the men behind the monsters) that that feature has really come into its own. While I haven't implemented it, I'd be curious if adding a house rule of reducing taken damage by [proficiency]d8 in the aura for spell-like creature features would work. Having said that, just having the conversation with your DM should help, hopefully they'll be thinking of you during their encounter designs and add spellcasters or creatures that can cast into encounters where it fits.

I think this mismatch will likely be fixed in OneD&D, as the Ancients Paladin is revised to have a more broadly applicable feature.

My suggested fix would be to make it resistance to all the common draconic damage types. Fire, Cold, Lightning, Poison, and Acid.

The simplest "patch" would be replacing it with resistance to some relevant type of damage like poison or something for example. Not as unique of a feature but a lot simpler and requires less ambiguity.

This feature really is lackluster, especially given how it initially looks pretty strong.

How about something like the Nature Cleric’s 6th level ability, Dampen Elements, reworked into an Aura?

Starting at 7th level, when you or a creature within 10 feet of you takes acid, cold, fire, lightning, or thunder damage, you can use your reaction to grant resistance to creatures of your choice within 10 feet of you against that instance of damage.

So, it’s more limited in range than the cleric’s (10’ vs 30’), but you have the option of applying it to multiple people if they all get hit by the same elemental damage, so it should still work for spells. Shame it won’t work against Magic Missile or other force / bludgeoning damage spells anymore though. Maybe you could put “force” in there as another option…but that could probably lead to cheese, since on-demand resistance to force is likely to open up some abusive interactions (like make Staff of the Magi a much less suicidal nuke).

It’s also balanced somewhat by the fact that a paladin’s reaction is more useful than a cleric’s usually.

The simplest answer is probably just that the DM is more generous with what it works against. It doesn't have to apply to all damage that's magical, like magical weapon damage, but I think it's pretty easy to reasonably say "This enemy mage is using the 'ball of fire' action in their statblock, sure that counts as a spell." If it still feels underpowered, be more generous with it. If it feels overpowered, be less generous with it. Might take a little tweaking but there's a sweet spot in there somewhere.