Time Machine restore files of my previous iMac on new Mac Mini

[al404]

I did move from an iMac Intel to a Mac Mini M1
I did use the same TM disk but I did not restore from TM backup since I was moving from intel to M1

When I first connected my TM disk macOS asked me if I want to inherit previous backup and I said YES

I can see on the right hand side older bars from when I started backing up the Mac mini but I don't know how to access them

I'm sure that I did the same thing on previous macOS when moving from an iMac to a new iMac
I can't really remember very well but was nothing like displaying computer and I could select witch back up I want to browse

 

[plyle]

I restored my apps from my 2015 MacBook Air (Intel) to my new 2021 16-inch MacBook Pro (Apple silicone) with no problems at all. Use the Migration Assistant.

 

[HDFan]

I can see on the right hand side older bars from when I started backing up the Mac mini but I don't know how to access them

Not sure I understand the problem. When you are doing a TM restore you select the date bars on the right. Depending on Media, backup size, etc. it can take a long time before you can select an earlier date. Check the disk access light. If it is flashing then wait until it stops. You should then be able to select a date.