I think your problem is the keyslots holding the keys to the container - those keys are not part of a timeshift’ed backup - they only exist as part of the container.
The most trivial solution would be to use clonezilla to create a copy of your old disk - then write that to the new disk. There methods to expand a LUKS container - the Arch Wiki will be most helpful in that regard.
A timeshift’ed backup is usually not encrypted - that is unless you backup into another LUKS volume.
A timeshift’ed backup does not backup a user’s home - so unless you have a complicated system configuration - or want to re-create a Plasma 5.27 - there is simpler methods move to a new system.
- Presuming that all your important files, documents etc. is located elsewhere.
- Presuming the only goal is to restore the system’s applications with your personalized configs.
Your customizations is all stored in your home
- ~/.local
- ~/.config
And depending on your specific usecase other hidden folders and files may be applicable.
Then generate a list of packages - one for native packages (the official repo) and one for any custom packages.
Your copy of the configs and the package lists is all that is needed.
I once created a script for it - see → [root tip] [Utililty Script] Backup configuration and package list