TimeMachine – Does It Backup iCloud Drive Files?

No, these files are not backed up by Time Machine.

iCloud has its own deleted file recovery, available from iCloud.com Settings → Restore Files, but this isn't a substitute for backups since modified files are not stored, only those deleted completely.

Since you say that the 200 GB of pictures and movies are irreplaceable, I submit that it's worth the small expense of buying a 200 GB or larger external hard disk, so that you can first extract the files you want to keep to this disk and verify they are present and correct before trying to transfer them to iCloud Drive.

I'm not familiar with tmutil but it sounds as if you should be able to access the files from the backup using Browse Other Backup Disks as described in various answers to this question:

Before going into Time Machine, open a Finder window and choose "Computer" from the Finder's Go menu. (That's the key to being able to browse another computer's backup drive.) Then hold the option key and choose "Browse Other Backup Disks".

iCloud Drive used with the Store in iCloud option described here should be able to store your files in the way that you want but I don't know how it behaves if you try to copy a large amount of data (which is more than the free space on your local disk, if I understand correctly) in one go. You might have to copy the files in chunks that will fit on the local drive and wait for iCloud Drive to copy them and free up the space again before copying the next chunk. Alternatively you might want to look at alternative cloud storage services like Dropbox, where you can upload files through a web interface into a folder that doesn't automatically sync back to your local disk.