Look for a scuff mark on the tire (probably on the left side).
While squeak, clicks or chirps synchronous with pedaling usually indicate a crank/bb related problem, that isn't always the case. One other thing that changes with pedal motion is chain tension, which rises and drops twice per revolution. So if, for example, you have a broken axle, or loose cones, the wheel will shift to the left whenever chain tension increases. This doesn't show up on stands or trainers because the tension isn't high enough.
Another likely related cause is a broken axle. A broken QR axle is often misdiagnosed as just about everything else, because the QR skewer holds it together making it not obvious even if you remove the wheel. But it allows flex with chain load, and the chirp can come from within the hub as the broken axle deflects and rubs the shell.
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