Transfer everything from one computer to another computer

iMac mid-2017 13.6.9 failed. A year ago I started using an external SSD. Initially I installed an earlier version of Ventura, maybe 13.4. I successfully but with some hiccups was able to complete upgrades during the year to 13.6.9. Last week when I attempted to upgrade from 13.6.9 to 13.7.1 the iMac stopped booting. Since I really wanted an internal SSD and I didn't want to make the switch myself nor did I want to pay to have the original iMac repaired, I decided to search for a used iMac that already has an internal SSD. So, I have purchased a used iMac, mid-2017 that already has 13.7.1 installed with an internal SSD 512GB hard drive. I have Time Machine back-ups available. My question: what is the recommended/optimal way for me to transfer the information from the prior iMac (specifically from the external SSD) to the current iMac? Dare I connect the external SSD that has 13.6.9 as the OS? If I do, how would I move everything? Would there be conflict because of the different OS ie 13.6.9 vs 13.7.1? Or do I use migration assistant to move everything from the Time Machine back-up? Or is there another alternative? I appreciate any and all advice. An additional note: I am submitting this query using my wife's MacBook Pro.