Microsoft Edge trying to start WinSCP when I'm trying to search something that contains "scp:"

title.

Well, that's rather Edge question than WinSCP question.
If you want to explicitly search, instead of processing the URL, start by typing ?.

But there's no problem before I installed WinSCP...

Because before, you didn't have any application that understood the scp:// URLs.
If you do not want WinSCP to handle the URLs, uncheck "Register to handle URL addresses" when installing it:
https://winscp.net/eng/docs/ui_installer_selecttasks
You will have to uninstall WinSCP first, before reinstalling it with the option turned off.