Boiling it down, then,
  • you only need a high-speed Internet connection to d/l the installer (or to use macOS Recovery in the event of a catastrophe),
  • upgrading your current OS SHOULD perpetuate all changes you've made on your new iMac since you bought it, and
  • your Time Machine backup is the answer to your other questions (although specifics are beyond my experience).
Regarding your 2013 experience, Carbon Copy Cloner is the only means of which I'm aware to back up a Recovery drive (which is not part of your original installation other than in the sense that "it came along for the ride").

The new Great Equalizer is the SEND button.

In Memory of Harv: Those who can make you believe absurdities can make you commit atrocities. ~Voltaire