@Viet Tu Vu, Thanks for posting in Q&A. Based on my researching, all SMS messages will be sent through your default SMS app in the private space, even if you find an app that works in the Work profile. The article you find can be the cause.
To hide the messages app, you can try the methods in the following link to see if it works:
Note: Non-Microsoft link, just for the reference.
Hope the above information can help.
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