[chore] Expose move endpoint again, small settings panel fixes

[tsmethurst]

Description

If this is a code change, please include a summary of what you've coded, and link to the issue(s) it closes/implements.

If this is a documentation change, please briefly describe what you've changed and why.

• Reattach move client API handler
• Update settings panel a little
• Return nicer error when trying to move to a different account than the one you've already moved to

Checklist

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If this is a documentation change, only the first checkbox must be filled (you can delete the others if you want).

• I/we have read the GoToSocial contribution guidelines.
• I/we have discussed the proposed changes already, either in an issue on the repository, or in the Matrix chat.
• I/we have not leveraged AI to create the proposed changes.
• I/we have performed a self-review of added code.
• I/we have written code that is legible and maintainable by others.
• I/we have commented the added code, particularly in hard-to-understand areas.
• I/we have made any necessary changes to documentation.
• I/we have added tests that cover new code.
• I/we have run tests and they pass locally with the changes.
• I/we have run go fmt ./... and golangci-lint run.