There are a few ways to approach this.

Individual relays/contactors (with 120v coils) triggered by the under-bench switches, with multiple runs of 120v wiring back to your shop vac. . .

You'd need one relay for each of your tools. Pretty straight forward, but a bit involved, and not necessarily cost-effective. You could use something like these gadgets from Functional Devices:

https://www.amazon.com/dp/B000LEUJU6

Or, if you want local control at each station:

https://www.amazon.com/dp/B008FM5IN4

Alternately, you could use a low-voltage approach, assuming you had an available switched outlet at each of your tools. With this method, you would use a single relay (just like the ones linked above) to turn on your shop vac.

At each tool, you'd plug in an inexpensive, 24v (DC) power supply, and run the low voltage wires back to your shop vac relay.

An single diode pack keeps the low voltage power supplies separated. This particular one could handle feeds from 4 separate tool stations:

https://www.amazon.com/dp/B08NHJT51J

When you turn on your tool, the power turns on, and triggers the relay. Don't want the switch to activate your shop vac? Unplug the power supply at that tool. This method would be much more cost-effective.

I'm sure other folks will chime in with other suggestions as well. . .