Could do it with a power-measuring smart-switch on the router? Should be relatively easy to detect current being drawn by the router and then have an automation to do whatever like turn on the vacuum. Can have it turn the vacuum off after a minute of no router current draw, etc.
I guess it depends on how much automation you actually want.
This could definitely be done with smart plugs on each device - power monitoring would be a bonus as well. Use a unique plug with each device and a plug on the dust extractor. (Nothing would need to be done with EstlCAM - smart plugs would work for anything using those devices without requiring specific integrations/code).
When one of the switches goes on (or power monitoring shows usage), trigger the smart plug on the dust extractor.
Do the same in reverse to figure out when to turn it off.
There are some other more ‘technical’ ways (current sensors, blah, blah, blah) to do it with HA but why over complicate it?
Pay attention to power requirements and use an appropriately sized smart plug for the device being controlled. Amazon has several options for 20A handling - assuming you are on a 20A circuit, it would give you some overhead to handle device startups surge. Depending on type of dust collection you have, you’ll likely need a higher rated smart plug there as well.
Could also automate blast gates using one of the DIY blast gate projects compatible with HA. Some of those are using ESPHome which makes it pretty easy to integrate.