Are plugins instantiated on every request to WordPress?

Instantiate in the strict sense is to create an instance of an object from a class. Plugins aren’t necessarily class-based, so I’m not entirely sure what you mean by instantiate.

That said, WordPress includes the main plugin file for all active plugins on every front end and admin request. Whether this “instantiates” your plugin depends on where that instance is created (or what you mean by instantiate).

Plugin interaction with WordPress core happens via actions which you hook functions or methods to. Some actions run on both front end and admin requests, others run on only front end or only admin requests, and some can run multiple times within a single request.