Update: I was able to solve this problem. Thank you to everyone who looked at my question.
The problem was that the point cloud data was fixed. After unlocking it, I was able to move the data as intended.
For anyone who might face a similar issue, these Japanese support articles were helpful:
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Auto-registering data from SX10/SX12 (TBC-019): https://3dcx-supportzendeskcom.zendesk.com/hc/ja/articles/4408106669977
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Moving a point cloud using station coordinates (TBC-056): https://3dcx-supportzendeskcom.zendesk.com/hc/ja/articles/123230117563