What skill/tool/attribute to weave baskets?

[ProsecutorGodot]

Personally I'd simply call it a proficient dex check. There's nothing wrong with just having it be under additional proficiencies. There doesn't seem to be a whole lot of overlap with any existing skill.

Weaving a basket requires patience and attention to detail, more than manual dexterity. I've woven a basket before, and I am uncoordinated as hell.

So...there's a solid argument for a Wisdom check...

I'd instead argue that the check requires proficiency to perform, much likes thieves tools act in most cases.

This is going to sound quite restrictive, but I might actually go so far as to say you should have proficiency in this specific type of weaving. It wouldn't be a horribly exhaustive to get this proficiency, probably something given to devout followers as a default. Something the race could have as a default proficiency to reflect that.

[Greywander]

I like the idea of a general Crafting skill for simple things not covered by tools, but the niches covered by tools makes it seem kinda... pointless?

On the contrary, a "MacGyver" skill seems like it would tend to be really useful, particularly in a situation where you don't have tools or no one has the requisite tool proficiency. There are limits to what you could do, but those limits are a lot higher than if you didn't have this skill. A general arts and crafts/handyman skill would be like the Prestidigitation of crafting. Not everyone might see the point of such a skill, but the same could be said for a lot of things in the game. Not everyone gets as much mileage out of Minor Illusion, Prestidigitation, or Find Familiar. I guaranty that there are people out there who would find such a skill useful for a character concept they have, and would get mileage out of using it in-game.

Of course, since this would be a homebrew skill, there's not really a reason to include it unless someone at the table specifically requests it. I'm just making a case for why someone might make that request. I might also add it to my own list of houserules.

[Asisreo1]

Yeah RAW there is no check for crafting. You just make 5gp progress /day /proficient crafter. By strict RAW, you can only make 1 item per day, and everything takes 8hrs at least, but I think any reasonable DM should allow pro-rating. If a basket is 5cp, I'd let you make 100 a day, about 5 minutes per basket.

Late correction:

The rules allow you to make multiple items in a day so long as the sum of the items crafted are worth less than 5gp.

By RAW, you should be able to craft 12 baskets within a day.

[Sigreid]

Having taken several survival courses over the years, basket weaving is a surprisingly important part of it. I'd use Survival.

Edit to say: You can totally make baskets without any tools whatsoever.