Enforced by the database, not by a warning
There is a real difference between a system that warns you about a clash and a system that cannot record one. A warning can be dismissed by a tired person at 6 PM, or missed entirely by a patient booking at midnight on your website.
Room and equipment clashes are prevented the same way practitioner clashes already are: by the database refusing to hold the same resource twice at the same time. Velvet Lead runs on Postgres, and this is one of the things a proper database is genuinely good at. It is the same principle as the roles and permissions that decide who can see what.