Contacts, Calendars, Notes, Reminders, etc. are not included in an iCloud backup.
Messages have always been a part of the backup but there has never been an option as to whether to include them or not.
You can see what is taking up the storage by going to Settings>your name>iCloud>Manage Storage>Backup>click on your device (if you have more than one device listed, you will want to review what you are backing up on each of those individual devices as well). You can also click on any of the other devices and remove their backups altogether.
But Messages have always automatically backed up to iCloud, and Messages can take up a ton of room in the backup. Here is a list of what iCloud backs up:
- App data
- Apple Watch backups
- Call history
- Device settings
- HomeKit configuration
- Home screen and app organization
- iMessage, text (SMS), and MMS messages
- Photos and videos on your iPhone, iPad, and iPod touch1
- Purchase history from Apple services, like your music, movies, TV shows, apps, and books2
- Visual Voicemail password (requires the SIM card that was in use during backup)
Your iPhone, iPad, and iPod touch backup only include information and settings stored on your device. It doesn’t include the information already stored in iCloud, like Contacts, Calendars, Bookmarks, Mail, Notes, shared photos, iCloud Photo Library, My Photo Stream, Health data, and files you store in iCloud Drive.
So, it may or may not be your Messages that are taking up so much room. Do they have a lot of photos and videos in them? Have you considered moving those photos and videos to your photos app and deleting them from your Messages?