The Jira cloud documentation says "Click Delete to remove an option that has not been used." (https://support.atlassian.com/jira-cloud-administration/docs/edit-a-custom-fields-options/) This clearly means that an attempt to delete an option used by at least one issue should be refused.
There is no similar documentation for Jira Server. This page, for example, does not go any farther than saying that options can be edited: https://confluence.atlassian.com/adminjiraserver0820/configuring-custom-field-contexts-1095777015.html. I can't find any more server documentation than that.
What I experience in JIra Server version 8.20.10 is the following warning:
Confirm that you want to delete this custom field option Earth.
Note: Deleting a custom field option removes all matching values from all issues.
Issues with this value 1
After confirmation the option is removed from that issue.
It looks like the cloud documentation is simply wrong and the action is possible. Or Jira cloud and server simply handle this situation differently. I'm not in a position to check Jira cloud.
BTW, the server page has dire warnings about editing options: "When you edit the values in your custom field configuration, you should manually update the values in existing issues. If you don’t do that, then as soon as you edit an issue the custom field values will revert to null or the default option on the issue page." This simply isn't true. You can, for instance, change the value of an option and the new value is immediately seen in issues.
Does anybody understand what is going on here?
>Or Jira cloud and server simply handle this situation differently.
Yep, that's the crux of it. Different software, different ways to do things.
The "dire warnings" are sort of right, but also out of date, as you say. It's perfectly safe to rename an option in a (multi-)select-list now (including radio buttons and checkboxes).