I would like to change the base URL of our Jira and Confluence cloud instance. Would it be possible to do that without having to migrate to a new site?
No.
Atlassian have it on the to-do list, and have not said they won't do it, but at the moment, you still have to migrate to a new site.
HI @Duong Pham
Welcome to the community!
Adding to @Nic Brough -Adaptavist- answers just to have a look at the below issue. It's related to changing base URL for cloud instances.
https://community.atlassian.com/t5/Jira-Service-Desk-questions/Changing-Base-URL-of-cloud-JIRA-Service-Desk/qaq-p/820345#M16324
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