Finder will not launch on 2024 Mac Air

I'm confused how you can relaunch the Finder if the Finder does not even launch to begin with. However, I understand you were able to set up the new Mac to the point at which you could at least begin transferring content manually, so it must have been working at one time. At some point the Finder became unresponsive and it's doing nothing but spinning. Is that all correct? If that's the case you might be better off erasing the Mac and setting it up again as new.

Migration Assistant really is the best way to set up a new Mac and I encourage you to consider doing it that way. We can address any quirkiness on the older one, or the new one once MA finishes.

Either way, without a functioning Finder, I think the only way to get anywhere will be to erase the Mac in Recovery mode, after which you can decide how you want to proceed. Instructions: Use Disk Utility to erase a Mac with Apple silicon - Apple Support. You will probably want to skip the preliminary steps (install updates, create a backup, etc).

I'm wondering if it has something to do with enabling Desktop & Documents in iCloud: Add your Desktop and Documents files to iCloud Drive - Apple Support, and if that's the reason you mentioned the 64 GB on your Desktop. That much can certainly take a long time to synchronize. I am also assuming you purchased enough iCloud Storage to accommodate all that. Does any of that sound relevant?

iCloud Desktop & Documents would also mitigate the need to purchase a Mac with an abundant amount of local storage, in which case choosing 512 GB starts to make sense to me.

If I'm wrong about all that then go ahead and erase / start over again. Otherwise I'd contact Apple because perhaps something else is going on: Official Apple Support

Quick question: how new is that MacBook Air? The reason for asking is that 512 GB isn't that much any more, and obviously attempting to fit 2 TB of content into a 512 GB Mac isn't going to work. You have 14 days to change your mind and return it for a larger capacity Mac. Bear in mind even if you have somewhat less than 512 GB of content, that won't leave any room for growth. Your previous Mac is now about ten years old, and it's reasonable to expect its replacement should last at least as long.

When using Migration Assistant, you can choose among a broad categories of items to transfer. I'd find out what you can live without on the older Mac, and delete those items before migrating its content to the new MacBook Air.

You should also have a Time Machine backup of the older Mac, which ought to go without saying: Back up your files with Time Machine on Mac - Apple Support

Aha. That's a lot of data to sync, so perhaps there isn't anything wrong after all. Still, it would be nice to have some overt visual indication progress is being made... other than the "beachball" which tell us nothing.