Being more the wrench spinner type than an electrical guy, I know what a suppressor is on a gun, but a suppression diode? Ya got me there, E.
Ric
Howdy;
NP, sir. Pitchers' worth a few hundy words ...
Suppression across contacts/load:

Suppression across relay coil:

One protects the 'relay 'trigger' ( e.g, whatever's driving the relay coil); one protects the contact / load. BackEMF is very bad juju.
Possibly overkill in this instance, Unless one is implementing a huge airhorn compressor, lol. But - the magic's in the details. Guilty. Use a 1N4007 ( 1 amp, 700v PIV ). Stout.
Cheers
E