Why wouldn't you do that? If you're going to do it, do it right.
It's a $75 card. It's going to bottleneck on games.
https://www.newegg.com/Product/Product.aspx?Item=N82E16814202237
The stats aren't all horrible on it but increasing the GDDR will reduce some of the problem and is a cheaper replacement than a faster clock speed, etc.
I honestly think OP's biggest bottleneck is the 5400 RPM HD. Swapping that for an SSD should eliminate most of the problems. They're like $100 for 1 TB so it wouldn't be an expensive upgrade.
And just to throw it out there: "budget" always comes with bottlenecks. I mean, yeah, we all know that but it's easy to build a rig and go "this isn't as nice as I thought it would be" while we forget why we bought budget components in the first place. It's a shiny new computer and we always hope for better than we bought.
You don't need that much unless you're gaming at really high res and maxing the fuck out of every game's video settings. For me a RX 580 with 8 gigs DDR5 has ben wayy more than enough