This right here is our fundamental point of disagreement. I don’t believe for a second that this is a rule the writers consistently abide by.
Your 'belief' is not mirrored by their express language on Sage Advice.
See also: 'Melee weapon attack' as opposed to an 'attack with a melee weapon' having very different meanings when they appear in rules text (and that terminology being deliberately chosen).
Same deal with the terminology of 'a target you can see' (and its effects) or the terminology of 'attack' and their meanings, or 'creature' or 'unattended object' instead of simply 'target' or whatever in the text. It has definite (and intended) game meanings.
I cant rule out that the Devs slipped in a 'melee weapon attack' instead of 'attack with a melee weapon' by mistake somewhere, or screwed up and unintentionally omitted the words 'magical' from an abilities text somewhere, but the reality is THAT is what they do, THAT is what it means when you see it (or dont see it) in the text, and THAT is how it is supposed to work.
------------------
Assume I am writing a class feature for a new Paladin archetype (Oath of the Hospitalier). The Class feature im working on is called 'Sacred Vitality'
Version 1: As an action you can call out to your allies seeking to magically bolster them against harm. When you do so you may restore hit points to any number of creatures of your choice you can see within 30' of you that can hear you. Affected creatures regain a number of Hit Points equal to your proficiency modifier x 5 up to their maximum number of hit points.
After you use this ability, you cant use it again until you finish a long rest.
Version 2: As an action you can call out to your allies seeking to bolster them against harm. When you do so you may restore hit points to any number of creatures of your choice you can see within 30' of you that can hear you. Affected creatures regain a number of Hit Points equal to your proficiency modifier x 5 up to their maximum number of hit points.
After you use this ability, you cant use it again until you finish a long rest.
Version 1 is 'magical' (by virtue of the
inclusion of the word 'magical' in the rules text). Version 2 is not magical (by virtue of the
omission of the word magical in the rules text) and thus can be used in an AMF.
-----------------
That is what the Devs have said they have done. If they intended something to be magical
they will tell you the thing is magical in its rules text. If the words 'magical, magic or magically' is not in the text, it is not magical (unless it is a spell, mirrors a spell, or is powered by spell slots).
Pick up your copy of Tashas or the Monster Manual and read through the Archetypes and Monsters and the various class features and monster abilities as written; you'll see the words 'magic, magical or magically' literally contained in many special abilities. The inclusion (or omission) of the word 'magic, magical or magically' was not put in the text of those abilities by mere chance or artistic licence of the writer. It was deliberate choice and has an intentional rules impact.