What is the Avenging Angel Aura of Menace save DC?

Question

The party paladin (Oath of Vengeance) is currently 18th level and we are planning on playing to 20th. Eventually he will get the Avenging Angel class feature, which states, in part:

At 20th level, you can assume the form of an angelic avenger. Using your action, you undergo a transformation...You emanate an aura of menace in a 30-foot radius. The first time any enemy creature enters the aura or starts its turn there during a battle, the creature must succeed on a Wisdom saving throw or become frightened of you for 1 minute or until it takes any damage.

There is no DC specified for for the Wisdom save.

As a paladin, the character's Spell DC is 8 + Proficiency bonus + Charisma mod. This seems like the obvious DC to use. However, in terms of RAW, this ability is not a spell. In fact, I don't think it even meets the Sage Advice litmus test for a magic ability¹.

The DMG gives rules for casting a spell from a magic item when you don't have the Spellcasting ability, but in this case the paladin is not casting a spell and does have the Spellcasting ability.

The Avenging Angel class feature appears similar to the Draconic Presence class feature, which also does not state a DC. The sole-and-accepted answer to this question about Draconic Presence argues for using the Spell Save DC because the Draconic Presence is both fueled by sorcery points and lasts "For 1 minute or until you lose your concentration (as if you were casting a concentration spell)". The Avenging Angel feature is not powered by spell slots (or even a Channel Divinity use) and maintaining it does not require concentration.

I think using the paladin's Spell Save DC is a reasonable approach, but I wonder is there any RAW for setting the DC of a non-spell ability when none is specified?

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¹_{It is not a magic item, not a spell, does not create the effects of a mentioned spell, is not a spell attack, is not fueled by the use of spell slots, and is not explicitly described as magical.}

Answer 1

The spell save DC is the only thing it could be.

The description of the Paladin class states:

Your choice grants you features at 3rd level and again at 7th, 15th, and 20th level. Those features include oath spells and the Channel Divinity feature.

[…]

Some Channel Divinity effects require saving throws. When you use such an effect from this class, the DC equals your paladin spell save DC.

The description of Channel Divinity has a line to account for the save DC of Channel Divinity features. This is the closest thing to a rule governing the save DC for the Paladin’s 20th level feature. No other rule even comes close. It should be obvious: use your spell save DC.