32 servers and 1 TinyPilot

Of note to the OP @alex123 , you can control the TESmart units via IP, so if you can connect them to your network, you could possibly stack them with two 16 port KVM switches plugged into an 8 port KVM switch. I haven't tried these stacked (and don't have a justification for the cost of buying more to test it) but it might work? 😅

Use the Windows-based (ew, but at least it runs under wine -- tested with q4wine) configuration utility to configure their IPs appropriately for your network and then you could whip up a crude web management page that controls them more cleanly -- I wrote something in PHP that can successfully manage my 16-port switch. You could translate the UI into something cleaner where clicking one button sends the relevant commands to both switches (e.g. 32 numbered -- or even named -- buttons that send a command to the "front" switch to use port 1 or 2 appropriately, and another command to the relevant "rear" switch to select the appropriate port).

If stacking these does work, the bonus is you'd have six open ports on your "front" KVM for extra devices, and in theory could attach six more 16-port switches to manage up to 128 devices (or to be really insane, use a 16-port switch in the front too and manage 256 devices!)

You could always buy two 16-port switches and temporarily stack them to see if it works. If it does, get the 8-port one and go at it; if it doesn't, you could get a second TinyPilot and have each 16-port switch on its own TP (so you'd have to browse to TP1 for ports 1-16, and TP2 for ports 17-32).