MacBook Air (3,1) - Worth It?

Found an old MacBook Air 3,1.. Now I remember why I stopped using it. The battery is dead. Can only operate while directly connected to power.

I guess I have a couple of questions.

The performance on the old gal is very lackluster. I don’t, nor, would expect much at this point. However, how much of that is due to it only running off of direct power?

If replacing the battery will negate what I think is impacting performance… is it worth going through the update process? Software and features aside. Has anyone done this (with a comparable Mac) and how well does your system run?

And just as an aside. The comp is completely up to date running High Sierra 10.13.6 😉

Thanks in advance!