Time Machine Restoration, External SSD, White Crossbars… huge headache

I’m unable to open a restoration of my system, hosted on an external SSD, as I’m getting the white circle with a crossbar. My late 2019 Mac, Intel, has two main partitions, one hosting my original (as hosted on the machine originally) Catalina system and the other hosting my current Sonoma. The current partition is out of room, and I must offload the original for space. I have an external SSD with plenty of space. Before doing anything I backed up to a second external to keep my Sonoma and Catalina spaces. To offload the Catalina, I partitioned the primary external, restarted in recovery mode, and opened Time Machine restoration to take the newest Catalina backup and restore to the external partition. I enabled boot up from external hard drives. Restarted, and selected the external restoration. I was treated to the white crossbars and a multitude of restarts, not of my request. I restarted in recovery mode, did a first aid on the restoration, and found nothing wrong in either volumes (the restoration primary, and the restoration “ - Data”). What can I do to get this working? I tried a few months ago to restore a very early Catalina backup and received similar failures