To my knowledge, it’s customary for artists to charge based on how much work is involved. So, they’ll calculate a wage for themselves and multiply it by the hours of work + material cost. Usually, that wage is relatively low, i.e. close to minimum wage, if your country has that.

So, you can try to roughly estimate based on that. You’ll probably forget some of the work needed to actually create it, but at the same time, artists are usually also quite quick at their craft.

However, you can also ask for a rough estimate upfront. It’s not going to be that artist’s first rodeo, they’ll probably have a pretty good guess, and they understand that people do care about the price.
And if something unforeseen happens, which means significantly more work is required to make your idea happen, then they’d hopefully also inform you about that and offer you cheaper alternatives.

Having said all that, if you are getting art made, then it is a good idea to have money to spare, even just for your personal finances.

On comission sites there can be an average price for each artist; you can then add the complexities you want around the art and increase the price based on how difficult it can be in your head. Most of them also list how much art corrections go for, or how many are included.

As for the file format; most hat manufacturers will accept PNG format; but you can also have the PSD in case they don’t so you can convert it easily.

I mean, at the end of the day, I just want a hat, and at least a guestimate on its cost.

I’m in awe of the direct links to anything. However, man, people assume the top result of DDG an impressive amount.