If you do mean XenServer, well - yes some large places are still using it but it's definitely dying out after they proved very slow to deliver new features then put a restriction on free / open source users as of 7.3 onwards that prevents clusters great that 3 hosts rendering mostly useless.
XCP-ng (https://xcp-ng.org/) is a fork of XenServer which is picked up where XenServer left off and is doing a lot in a short period of time (IMO) to add new features and build / support the community.
Majority, but the latest generation ("nitro") uses KVM.
(And though you're correct with regards to the question, I don't believe AWS uses Citrix's XenServer.)
There are generally two big FOSS hypervisors (Xen, KVM), a bunch of smaller ones (bhyve, vmm, the one in l4) and the somewhat-open ones like VirtualBox-OSS.
Then again, the whole local setup scope is a niche in itself.