Hi,
It would depend on which versions you start with during the migration. Many recent applications (Intel 64) can run on an M1 Mac now under Rosetta 2, without being a Universal 2 binary updated for Apple Silicon.
I recently acquired an M1 Mac mini, and a lot of software already works even though it hasn't be updated to run natively. But, there is a lot of software that cannot be used yet - things like Logic/Pro Tools audio plug-ins, disk maintenance utilities, etc.
I personally never do a data migration from one Mac to another. I always set new Macs up with a clean slate, and manually migrate anything I store on the internal drive, as most of my files are on external drives.
Are there any applications in particular you are worried about?
C