Enable vue/no-mutating-props rule

What does this MR do?

Existing violations of this rule have been specifically ignored, as fixing each one requires non-trivial work to fix.

Addresses #297222 (closed), part of &5168.

Screenshots (strongly suggested)

n/a

Does this MR meet the acceptance criteria?

Conformity

• [-] Changelog entry
• [-] Documentation (if required)
• Code review guidelines
• [-] Merge request performance guidelines
• Style guides
• [-] Database guides
• Separation of EE specific content

Availability and Testing

• Review and add/update tests for this feature/bug. Consider all test levels. See the Test Planning Process.
• [-] Tested in all supported browsers
• [-] Informed Infrastructure department of a default or new setting change, if applicable per definition of done