Hi jury-city,

You might see instantly that the 2024.1 FBX export produces much smaller file sizes based on the missing data. This clearly shows that the exporter in 2023 should be used for now.
I hope that is an option for you for the time being. In other words, the scene you use does not use any features that are only available in 2024.

Sorry, I have no workaround other than how you described opening the 2024.1 file in 2023 and exporting from there.

The FBX import from 2023 to 2024.1 works

Fingers crossed, a working version will soon be available for you.

All the best