First off, when you say "a 50% crop" you are usually referring to linear measurements. This is certainly the case when comparing a FF sensor to a micro four-thirds sensor. The linear size of the µ4/3 sensor's diagonal is exactly half that of a FF camera with a 36x24mm sensor. This means that the area of a µ4/3 sensor is roughly one-fourth the size of a FF sensor.
Due to the difference in aspect ratios between the two formats, the actual difference is 225mm² versus 864mm² when the FF sensor is a full 36x24 mm. Many FF sensors are actually slightly smaller. The Sony A7R III sensor measures 35.9x24 for an area of 861.6mm².
If you do a '50% crop' of an image from a 42 MP FF sensor you do not wind up with a 21 MP image. To do that you would need to do a '71% crop'. This is because the reciprocal of the square root of two is approximately 0.71.
When you crop a 42 MP image from a FF sensor to the dimensions of a µ4/3 sensor, you only use about 11 MP. So the deck is stacked fairly heavily in favor of the smaller sensor if the lens provides more resolution than 11MP can provide.
On the other hand, if the lens in question is not capable of resolving details that can be rendered by a sensor with 11 MP in the area covered by a µ4/3 sensor, it wouldn't matter. The resolution of the lens would be the limiting factor in either case. At FF size this requires a lens that can outresolve a 44+ MP sensor. A few current lenses can certainly outresolve a 44+ MP FF sensor, but many lenses currently on the market or sold in the recent past can not.
I cannot tell if the subject (bird) will be the same size when each sensor readout is converted to pixels or not.
How many pixels the bird covers is determined by the pixel pitch of the sensor. The 42 MP Sony A7R III has a pixel pitch of about 4.5 microns. The 20.3 MP Panasonic G9 has a pixel pitch of about 3.3 microns.
If the image of the (let's assume a rectangular shaped) bird is projected by the lens onto the sensor as 10mm wide and 5mm tall it would cover about 2.47 MP (2,222 x 1,111 pixels) on the Sony Sensor and 4.5 MP (3003 x 1501 pixels) on the Panasonic sensor.
If you are viewing both images at "100%" (one image pixel per screen RGB pixel set), the bird would be about 35% larger linearly and cover about 82% more screen area. But whether the larger image reveals more detail would depend on the resolution of the lens - you might just be viewing larger amounts of blur.