The search for a "SketchUp Pro 2022 serial number and authorization code" is ultimately a search for trouble. Legitimate serial numbers simply don't exist for public distribution – they're unique to each paying customer and verified online.
Deauthorize an older workstation by going to Help > License > Remove License on the old computer before activating the new one. If the machine is broken or inaccessible, contact Trimble Support to reset your activation count. Offline Activation Issues --- Sketchup Pro 2022 Serial Number And Authorization Code