1. Use timeshift to create a backup of your current system - make sure you include your hidden files.
2. Do an install on your new drive - just the minimum
3. Start up the new system and use timeshift to restore the timeshift backup to the new drive - it will overwrite as required and restore your local configs.
You now have you old system on the new drive with all the installed software and matching configs
Copy data from old drive or backups as required.