reinstalling Mac OS keeps also the wi-fi router passwords or not ?

If you erase the the startup disk and do a fresh install of macOS the wifi passwords have to be re-entered.

If you install macOS on top of itself, the existing wifi passwords in the existing macOS install shoud remain.

If the above is not your problem, please expand on your problem.

This may sound like a dumb thing to say, but there can always occur an unexpected problem, due to who knows what? For that reason, I have always kept a separate list of all my passwords on an Excel spreadsheet. Yes, it has a password to open it as well for security. So if something ever goes wrong, I have them. And I can occasionally refer to that sheet when needed. I suggest you consider doing the same.

The macOS installation does not affect your wi-fi router passwords on the Mac.