There don't appear to be any official examples of this
You can filter a search on D&D Beyond for types of resistances/immunities and while you can filter for many very specific combinations of resistances/immunities, "nonmagical [damage type that is not BPS]" is not among them. Examples of some of the very specific filter combinations:
- Bludgeoning, Piercing, and Slashing from Nonmagical Attacks while in Dim Light or Darkness
- Piercing and Slashing from Nonmagical Attacks that aren't Adamantine
- Piercing and Slashing from Nonmagical Attacks that aren't Silvered
- Bludgeoning, Piercing, and Slashing from Nonmagical Attacks
The only options for resistances/immunities for other damage types appear to be a blanket resistance that covers all sources of that type of damage not just nonmagical sources.
For example the air elemental has
Damage Resistances Lightning, Thunder; Bludgeoning, Piercing, and Slashing from Nonmagical Attacks
This means that air elemental has resistance to lighting and thunder damage regardless of if the source is magical or not. Note also that the air elemental had a very low CR. The type of resistance/immunity would be a weaker form of the normal version and the we'd actually expect to see it more in lower CR creatures if at all, yet we don't.
While the D&D Beyond search is not necessarily perfect (those these filter options do appear to be all-inclusive in my shakedown) and it is impossible to prove a negative, this backs up my experience. I have seen many many monster stat blocks and I have never seen an example like you are looking for.
Thus I can state with reasonable confidence that there is no such monster present in official material.