Hi Stu,
If iCloud storage is maxed out, that can cause a variety of issues with synced data.
Check Settings > your name > iCloud . Show All > iCloud Calendar to see if it's on. If it isn't, these steps wouldn't't help.
iCloud storage, if you're on the basic 5GB plan, can be increased 10x to 50GB for USD$.99/month. Other plan pricing is here: iCloud+ plans and pricing - Apple Support. Increasing your space might resolve issues.
Before attempting anything, it's good policy to back up to a computer: How to back up your iPhone, iPad, and iPod touch - Apple Support
If you don't have a computer you can back up to, increased iCloud storage would be important so that iCloud backups work properly, and synced data (such as Contacts, Calendars, Photos (if enabled) Health, and more, work properly.
Jack