Will my calendar and contacts in iCloud be lost if I delete backups? I cannot do any new backups because my iCloud storage is full.

I want to switch to using my computer for backups and delete the ones I have in iCloud. However I don’t want to lose my contacts and calendar that are also stored in iCloud.
You can safely delete your backup from iCloud. To do this, go into Settings →  Your Profile →  iCloud →  iCloud Backup and turn the switch to Off to disable iCloud Backups.

This will only delete your iPhone backup from iCloud. It will NOT delete your iCloud contacts and calendars.