If the re-install ends up becoming an erase-and-re-install, the following (highlighted) section is where the Time Machine backups get migrated / restored / reloaded, as part of the first startup of the new macOS install.
Setup Assistant loads your content from the backup.

Note: If you decide to skip the first setup and skip running the setup assistant (setup assistant is effectively the same as migration assistant, run during the first startup, and which also migrates previously-installed apps), then pick your first newly-created login at first startup different than the login name you want to restore. If you have a login called MyName that you really want to use, do not create a new MyName at that first login after an erase-and-install, as now you won’t be as easily able to migrate your previous backup of MyName. Pick MyAdminName or other such name as that first new user after the erase-and-install, and use that, and then you can migrate in your MyName files later using Migration Assistant.