While that is the traditional lore, I think you're technically mistaken about the water. The MM says that the vampire takes damage if it ends its turn in running water. Meaning that it needs to be submerged.
That said, I agree that clothing wouldn't help. I don't think the water needs to touch the vampire's skin. A vampire is an unclean thing and running water is a symbol of purity. Hence, vampires are harmed by running water. It's more spiritual than physical IMO.
Although I have to wonder where one would even think to find waterproof clothing in a typical D&D setting? An oiled cloak is one thing, but it won't prevent you from getting wet if you get dunked in a river.
As to clothing to keep sunlight off, I agree. While we normally don't track damage to clothing in a typical D&D game, because it doesn't matter, it would matter for a vampire. Uh oh, fireball burned some holes in your clothing while you were standing in sunlight and now you're dead.
It doesn't need to be submerged - the exact wording is:
Harmed by Running Water. The vampire takes 20 acid damage if it ends its turn in running water.
If it meant "submerged in", it would say "submerged in", not "in". So if a vampire is stand ankle-deep in a stream, or waist-deep in a river, they take damage. I would say that being on a boat isn't "in" the water by any sane use of English, it's "on" the water, so they don't take damage there, but if they fall out they'd be dead in under a minute.
Re: sunlight, I think a vampire of this level of power shouldn't be protected by clothing. Lower-end vampires, recently-turned vampires, weaker vampires - I could see them being protected by clothing, but the full-on vampire statblock is a real lord of the undead, and he's clearly not "normally naked".
So the idea that clothing protects him, but they just forgot to put that in the statblock makes little sense. He takes 20 radiant/round in sunlight. I would say that assumes he is wearing clothing (as depicted, and as makes sense). It's not that he normally takes 80/round but wearing clothes over most of his body lowers that! Nor is it that 20/round is strictly for vampire nudists. Both are just silly.
Also if you start making up random house rules about vampire clothes, you run into stuff where spells designed to kill vampires with sunlight arguably shouldn't work or should be massively less effective because the vampire isn't a nudist. Trust me no-one wants to see Count Strahd's junk so don't go down the "clothes make you immune/reduce damage!" route.
If you want vampires to have a reason to wear high collars, big hats, sunglasses and so on, note that this 20/round is DIRECT sunlight - i.e. not reflected/ambient sunlight - so you could say if vampires don't wear that stuff, when they're getting significant reflected/ambient sunlight (i.e. bouncing off objects and the floor and so on) on them, that does maybe 5/round, or perhaps just causes them pain.