Do you use an MDM or any system that can deploy certificates? If so, I would look into using certificates for the staff devices.
In the Meraki world you have Systems Manager which can do this. You can do things like say only devices with Systems Manager installed can connect (so you would only put it on staff devices):
https://documentation.meraki.com/MR/Splash_Page/Systems_Manager_Sentry_Enrollment
You can also take it a step further (which I would) where you can get Systems Manager to deploy certificates onto the devices, and then using tags you can say only devices with a tag of "staff" are allowed on the staff SSID. If you used it with studeny devices you can apply the same logic to only allow students to access the "student" ssid. You can also kick a student off (say for a breach of policy) by simply removing the tag from their device.
Because this uses certificates there is no working around this.
https://documentation.meraki.com/SM/Other_Topics/Certificate-based_WiFi_authentication_with_Systems_...
For school assets you would normally make the device "fully" managed. For Apple this is called "Supervised" mode, and for Android it is called "Device Owner" mode.
https://documentation.meraki.com/SM/Profiles_and_Settings/iOS_Supervision
https://documentation.meraki.com/SM/Device_Enrollment/Android_Enrollment
Note that Cisco Meraki Systems Manager also integrates with Apple School Manager (in case you use that).
https://documentation.meraki.com/SM/Profiles_and_Settings/Configuring_Apple_School_Manager_for_Share...
I don't personally like using it, by Systems Manager also has a BYOD mode you could use with student owned devices. Note that BYOD mode can also be used to do lots of other things, but in this context I am only referring to it for configuring secure WiFi with certificates.
https://documentation.meraki.com/SM/Device_Enrollment/Containerization_with_Systems_Manager