steeldragons
Steeliest of the dragons
Well, for the first, I would never have/permit that....that an "oath," however heartfelt, just poof gets magical power. "Oath Magic" is not a type of magic that exists in my game/world.There's a few ideas I'm thinking of.
First is what's been discussed here; the idea of "oath magic" wherein some few people who swear with conviction and purpose in their hearts are granted power. No one knows the "source" of this power, no god or divine agent or other powerful being lays claim to being the source. There are various theories that exist in the realm of arcane research, but no one has a definitive answer, least of all these paladins themselves.
Second would be something like Eberron, whereas the characters in the setting will believe in the existence of various gods, but these gods' existence canonically is ambiguous.
An oath of "conviction and purpose in their hearts," as you say, "are /granted/ power." So it's coming from somewhere. You (the character) don't have to know, or even care, I suppose. No one in the game world has to "prove" where it comes from.
To my thinking, in the case of entities capable of granting "paladin powers/magic" that's gods. In my homebrew, that's solely Lawful gods, to boot. They would WANT the attention/notice. So, for my world/game, I would say something like a god of Valor or Heroes or Defense or some virtuous things would take notice when the paladin is making their oath, to a cause or virtue or promises that that deity would like or respect ...or even just could use for their own purposes someday... and "answer" by way of "empowering" the oath that is made. The paladin, again because /most/ gods in my world would want the credit, would be made aware that "These Powers are brought to you courtesy - and in furtherance - of..." Maybe not. But more than likely, yes.
To the second, that's fine/easy enough. Clerics are getting their power. The mortals have built up their religions, and mythologies, and churches to explain XYZ in their lives. Clerics devote themselves to these religions and churches...and poof they have magic. The gods work in mysterious ways, and all that.... Still, they are taken, in world, by people as "canon" even if they, meta-wise, aren't defined.
But still, the idea that one would manifest divine magical power simply by "belief" is not going to be a legit/satisfactory explanation in my game or world. There is going to be a source behind it, even if the sages can't pin down exactly whence or by whom it comes.