Insufficient permissions for drive access on macOS Seqouia with MacBook Pro and iMac

I cannot access any of my drives other than an old G-Raid 4tb but it is absolutely full and will not allow me to copy anything to one of my may other drives.i am told I do not have permissions on the target drives. if I try to change to read and write. I only get read only!!! I splashed out on a 10 tb hdd Seagate drive to try to move things about but it did 5 Time Machine saves and said It was full. I am using a brand new MacBook Pro and I am booting my old iMac mid 2015 from an ssd as I was loath to stop using the 27" screen that was still excellent. can anybody help please. Does the TM not delete as it updates? On my new laptop I am running Seqouia on my old iMac I can only run Monterey on my dear old iMac! forgive me I am 69 and I was a film editor that used Macs always for my business and for personal use having several Mac Pros but the old wheels turn slowly these days so any help is much appreciated. thank you

[Re-Titled by Moderator]

Original Title: No permissions Seqouia