I wanted to try this but sadly it seems my A7 iii doesn't record gyro data.

There are external devices that can be attached to the camera to record gyro data, e.g https://docs.gyroflow.xyz/app/advanced-usage/using-external-... I just ordered one a few weeks ago and haven't received it yet, so can't talk about personal experience, but there's no technical reason it couldn't work well.

Out of curiosity - how do you sync gyro data with video timecode?

My a7CR seems to be supported - will try this out later.

Some months ago I tested footage of my A7C2 on Gyroflow expecting to do visual stabilization, and found my camera has a gyro (didn't know about it) and automatically adds that info to the videos.

The result was pretty good and it was super easy to do it.

Just be sure to turn off any in camera stabilization to get the best results.