Wordpress - Do deactivated plugins slow down a WordPress site?

No it doesn't. At least, not on the front end, or in the back end in any non-plugin area. WordPress only loads files whose filepaths are stored in the active_plugins option in the database and ignores everything else completely.

Except in unusual cases having deactivated plugins only affects the performance of the plugin page in the admin, and only then a trivial amount (unless you have hundreds of plugins.) During the plugin admin page load WordPress scans all the plugins and then stores the list of active plugins in the database. Then on all other page loads WordPress inspects that list of plugins, not the plugins themselves.

The one caveat to this is if the deactivated plugin stored a lot of autoload data in the wp_options table and deactivating doesn't remove that data because doing so could cause a user to loose configuration options when they deactivate which they may want to do only for a few minutes which is a common approach taken when someone is debugging a problem with a site. However, if you are using a plugin that add so many options during autoload that it causes a problem them it's not a great plugin anyway.

If you do run into such a plugin and need to get rid of the options then this might help.