In real life, carriers and battleships are usually surrounded by destroyers, submarines, cruisers etc. In Star Wars movies, the rebels have a wide variety of ships of various sizes, while the Empire just has its gigantic Star Destroyers. In canon/Legends, did the Empire have classes of non-fighter/shuttle ships other than the Star Destroyers?
In The Mandalorian Moff Gideon also uses an Imperial Light Cruiser.
There are, though not much in the live action films. Most of these are seen in Star Wars: Rebels. Since it takes place well after the Empire has been established.
Imperial Light Cruiser (as seen in Star Wars: Rebels)
Imperial Interdictor (as seen in Star Wars: Rebels)
Imperial Listener Ship (as seen in Star Wars: Rebels)
And certainly more.
They do, though we don't see them in the movies. In the Expanded Universe (books, comics, video games, etc.), they have shuttles for carrying troops, patrol craft that are smaller and more maneuverable than Star Destroyers, and several types of carriers, frigates, and Dreadnaughts.
There are also several kinds of Star Destroyer, including smaller classes that originally came from the Clone Wars (prequel) era, and a few specialized types, like Interdictor cruisers, which project gravity well beams. These beams can prevent enemy ships from going into hyperspace.
For a full list, I'd recommend looking them up on Wookieepedia. Most of these haven't been seen in the films themselves, but they are a part of the Expanded Universe, and plenty of creativity has gone into creating them. I don't know how much of a separation there is between the Expanded Universe ships and the new canon ones, but both are available on Wookieepedia.
The "Lambda-class shuttle" is seen in Return of the Jedi.
Both the Empire and Darth Vader use the Lambda shuttles to travel between Imperial capital ships and the Death Star.
Source: Den of Geek, 25 Best Star Wars Spaceships
A clip from the film follows
In the Pre-disney expanded universe the Imperial Navy exploited a variety of ships. HOwever the empire Favored Star Destroyers for their intimidation. But the immense cost and logistcal burden forced them to adopt cheaper ships in outer rim worlds...
- Vindicator class cruiser: A 600 meter light (destroyer shaped) cruiser
- dreadnought class heavy cruiser: used in the famous Katana Fleet
- KDB-1, Broadside class missile cruiser (Game: Empire at war)