Cloning a Catalina Intel Mac to a M1

We're using an Intel Mac mini running Catalina as a build machine, running a lot of specific and custom software.

We want to update that build machine to Big Sur in order to build apps for the latest iOS, unfortunately we're out of disk space on that machine (128GB model).

Management took the opportunity to upgrade and bought a Mac mini M1 to replace it, expecting to clone or restore a Time Machine on the new machine.

We have a huge technical debt on this, the person building it has left and is no longer in contact with our company, so rebuilding manually on the new mac is not a realistic option without spending a lot of resources on it.

Is there any way to clone the filesystem on the new machine and have it work "out of the box"?

A direct clone is not going to work since only Big Sur and up is supported on M1 (if I remember correctly,) but maybe cloning on a bigger external drive, updating macOS, creating another clone of that and restoring it on the new machine?
Has that any chance to work?

You should be able to Migrate directly from one Mac to the other, over Ethernet/WiFi etc. The older machine doesn't need to be on the same OS* [otherwise you'd get really stuck if the old machine was simply no longer upgradeable]. This even works from PC to Mac, though without apps etc, just documents.

After migration you will see which, if any, apps couldn't be successfully migrated - this all without touching the original Mac.
See Apple KB - Move your content to a new Mac for full details.

*The Apple KB says to upgrade to the latest OS first, but this isn't necessary. I migrated an old High Sierra Mac Pro to a new Big Sur M1 iMac only a few months ago.