Nest thermostat and old HVAC
There are two red wires in your blower.  Assuming the one I labelled below is the one from the thermostat, and the other three wires I labelled are also from the thermostat, you have this wired correctly.
Don't use the O terminals.  The thermostat's smart fan controls won't work that way.
Make sure the wires I've labelled in the picture below all come together into one cable and that is the right cable, that goes to your thermostat.  The one I labelled &quot;NOT R&quot; should be unrelated to the thermostat.

If that is the case, you might have a defective thermostat.   The Nest can run the fan without the cooler but not the other way around.
If you have a voltmeter and continuity tester you can check at the terminal block whether the thermostat is doing what it's meant to do. Using my labels:  R to B should always be 24V-AC.  When the system is off Y to B and G to B should both be 0, when it's on they should both be 24V.  In your phone app, with the system off, you can start up the fan by itself and you should see 24V on G to B.  You can test for broken wires by removing any pair of wires from the thermostat mount, twisting them together, removing them also at the blower and checking continuity between them.
NOTE: Turn your breaker off before delving into the blower circuitry.  The terminals on the other side of the metal wall to the transformer are at 240V and are not covered. There may be a power switch nearby that shuts down the blower but does not de-energize all the wires in there.
Edit adding diagnostic
Make careful note of where the thermostat wires are connected and disconnect them entirely from the blower.  Then use a spare piece of wire to jumper together power, cool, and fan signals at the unit, like this:

Turn on the power, and the system should come on.  The fan should come on right away, and the cooling within a few minutes.   Then disconnect your piece of wire from the middle of those three terminals and the cooling should stop but the fan should keep running.   If that all goes as it should, you know the system is ok and the problem is in the thermostat or its wiring.  Otherwise you know the system is the problem.