Some weapons do.
i use Favonius lance on Xiao. Not highly recommended to some
as he needs much more crit rate than most characters.
But it helps give him his burst back.
Having energy recharge stats on your artifacts also helps.
What you need to look up is Energy particles.
As particles are what recharge your bursts.
But for Xiao and Hu Tao specifically they also need HP because their own bursts/Skills tank their HP.

This is usually for Spiral Abyss because Abyss has timers and you need to beat
it fast otherwise you won't get 3 stars or gems.
especially once you start doing where you are required 2 teams.
as you don't do it by the timer runs out but before then.

Some artifacts that are highly good for energy recharge is Emblem. But Xiao cannot use it because his abilities do not snap shoot[still figuring out what that means]. But Emblem, Nobless Oblige are good for sub DPS or support characters. I use 2 set emblem for Ayaka, as her Burst is a high energy cost of 80 and she gets her burst back very quickly without a cryo battery.

The higher the level the more important it will be basically.
For now you don't need it as much. But once you start getting to world level 5-6
you're probably gonna need it.

Energy recharge or f2p options are good.
But elementary mastery weapons are pretty useless. Like you don't need them.
They can still be useful for someone like Xiao tho because he can swirl elements.
But preferably having crit rate or energy recharge is best.
I got Favonius lance from wishing ages ago but never used it for anyone until I got Xiao. And since only his skill gives him particles, not his burst, it works very well for him. And especially since Ayaka also has 2 emblem so she also gets her burst faster.

i only took a few days off since i was so stressed from jury duty.
but since it's over i can relax at last and finally can play.
i am so pumped for raiden and ayato.

@Moi
Well it was much different than TV shows tell you it's like that is for sure XD
I was potentially going to be part of a grand jury but luckily
it cut off right in front of me so my row and behind me were free to go thank goodness lolol.

But all i did all day was fill out paperwork. tho i did not know i could write
what cases i would be uncomfortable with being a part of.

And i mostly listened to how a grand jury works and what it would be like, etc.
so me and this one woman just sat and talked and said this was very interesting LOL.

I had to use my sister's phone the entire day as i don't have my own phone.
so i was super paranoid of losing it.