What happens with the Guest OS’s on ESXi in the event of a power failure

The UPS software is able to fire off a script at a point of your choosing after switching to batteries. Simply use that script to send appropriate commands. Rather than shut down the clients you could tell VMWare to save the current system state of the clients. Alternatively, have the script send remote shutdown commands to the clients using something like shutdown.exe or psshutdown.exe. Once those command are fired off have the script sleep for a suitable amount of time (sleep.exe) before shutting down the host.

The brief interruption to someone's work is more likely going to cost less than buying and maintaining a desktop UPS. That's one of many reasons why many professional solutions are server based and centralized, as the service level can be focused there.

If there is a business justification with Return On Investment (ROI) in your environment, I would suggest a cost analysis between providing generated or battery backed power to the entire building versus buying individual UPSes for every workstation.

A server does not necessarily need to "support" a UPS, it's just a battery that's inline with the power source. Any "support" is going to be automatic shutdown or taking a preferred action in case of power loss.

The idea is to protect the equipment by conditioning the power as well as allowing the equipment to be properly shutdown in case of an extended outage. Depending on your budget, it is also often to maintain availability in case of power loss but with that service level you often have power generation in addition to a UPS.

A UPS is in addition to backups and has no direct correlation to backups beyond being a best practice within properly run IT infrastructure.

Without a UPS you could lose data, have hardware failure, and have system availability interrupted. It is often easier to find the ROI here than with workstations.