Upgrading From 13" Pro 2014 to M3.

My current Macbook is on Big Sur and won't go to Verdana etc. I am thinking of buying a Refurbished 14-inch MacBook Pro Apple M3 Chip with 8‑Core CPU and 10‑Core GPU. I do daily Time Machine backups. Is it simple to just recover to the new machine by selecting the last backup and get all my logins without doing anything apart from turning the new machine on and it detects the USB2 drive I have? Thanks.