how long can "Preparing backup take?

That depends on several factors. If it is the first backup, or if it is a follow on backup but the earlier one was done many weeks earlier, the preparing can take well over an hour. Having a long delay between the date of the previous backup and the current one can require even more time "preparing" than doing the very first one. If the backup disk is a slower rotational drive (and/or the internal drive is a mechanical drive as well), that slows the process down considerably. If you have recently installed significant software or updated or upgraded your operating system, that will increase the "preparing" stage to be as long as an hour or more. And lastly, if one has antivirus software running, that can add a huge factor to the time needed to perform Time Machine backups.

With several of these factors, a Time Machine "preparing" stage can take hours. But normally, when they are performed frequently, the "preparing" stage takes seconds to maybe minutes.