Uh... no. Why are you trying to make what a PC says about themself into a game mechanic? You're right, we are not playing FATE. This idea that a PC says they are "the best swordsman in the land" has NO mechanical weight, and is not used to satisfy any game conditions.@DEFCON 1 seems to be asserting that, in 5e D&D, a free descriptor can be the main component of action resolution.
All it is, is what the PC has seen of themself within the narrative. That's all. If this PC has won every fight they have ever been in within the story... then they decide within the story to claim themselves to be the best swordsman in the land. And as a DM I find that perfectly acceptable. Does it matter to me if they are only 1st level? Nope. Does it matter to me that the 'Guard' NPC statblock or the 'Kobold' statblock could be used to defeat this character? Nope. Do I ever have to present pointless random challenges of Guards and Kobolds just to defeat this PC and thus prove they aren't "the best swordsman in the land"? I'd be a pretty crappy DM if I did that, if I do say so myself.
Here's the thing... this is all baseline improv rules. 'Yes, And...' and all that. The player says "I want my character's story to be that they are known as the best swordsman in the land." And I go, "Okay! Yes! Sounds great!" And at that point, I begin working stories that help exemplify that narrative, while also creating obstacles for the PC that are dramatically challenging. Being the best swordsman in the land is meaningless if they never get to show it off or occasionally prove themselves. But this will only happen when it is dramatically important within the story. I'm NOT going to just have a random town guard show up to kick this character's ass for no reason just to prove that I could. Because I think that's dumb. And narratively unsatisfying. And a kick in the groin to this player of mine for no other reason than because I can. And when these dramatically important parts of the story show up... the PC will get to exemplify it. Or on the off-chance the PC doesn't win one of these fights, then that will result in a further exploration of the drama for this character when they have to deal with it down the road in the story.
And all of this can happen when the PC is level 20. Or level 10. Or even level 1. Because the mechanics do not dictate the in-game reality of the story. Can it enhance it? Sure! If your PC is a level 16 Battlemaster Fighter and I throw many of the random NPC statblocks at you, your character is probably going to kick all their asses... oftentimes many of them at once. And if that happens? Then great. But it's not a requirement. Not be a longshot.
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