Starter doesn't work all of a sudden

I am working on a 1984 GPz550 and I had it running just last week, but the air filters needed replacing so I ordered some new ones.

They arrived today and I replaced the filters without even taking the carb off so the only thing I touched were the old filters. I went to start the bike once the filters were on and the starter turned over a few times but then nothing. When I click the ignition, the starter doesn't even turn over anymore. The battery has juice (12.6V before turning key on, 12.3V after) and there is full voltage at the starter relay.

I've had this issue before on other bikes but have never figured it out. All the cables and wires look good, I couldn't find anything amiss.

Could it be the starter relay needs replacing? I struggle with diagnosing electrical problems so any help is appreciated!

How many volts does the battery show when you push the starter button?

12.3V - same as when I turn the key.

It should drop a bit, so it seems that something is disconnected. It could be something inside the starter button housing. Solder gets brittle as it ages and can come apart. The switch contact could be burned or broken. Could be a loose connection anywhere in the starter button circuit that just finally decided to separate.
Taking careful readings with your multimeter at several places in the circuit should help you narrow down the culprit. Is power getting to the solenoid (small wires)? To the starter button? In and out of the ignition switch?