One of the core offerings in AWS is EC2. Which are just shared (up to dedicated) virtual machines, and they start at a few dollars a month. I'm in no way suggesting a change to your setup, only pointing out that AWS isn't some mythical complex ecosystem.
Is namecheap running PHP8? That upgrade alone will net you a massive performance improvement over 5.x
No doubt AWS has options that could work for me at a similar price point. But I don't think it would be at all easy from what I've seen, and I'd have zero support. Compared to namecheap which basically helps me do anything I need via live help with actually useful people in my experience.
I once upgraded from a $2.50 a month server to the $4 server for a few other benefits I needed, and performance actually went DOWN at that server IP. I asked them to move me to a different one, just based on my "trust me bro, this is slower than before" and they did move me and performance returned.