Error code 0xC004E016 typically indicates a mismatch between the installed version of Visio and the product key you are trying to use.
Try this keys,
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ProductKey:2XN7Q-TQBH2-RBB6V-YC8JF-3DD7P
Description:Office21_VisioPro2021R_Retail
Sub Type:X22-53521
ErrorCode:Online Key
CheckedTime:2026-03-18 10:54:50 AM(UTC+07:00)
ProductKey:FRPHH-4TV2C-4JMBH-PHNXH-VVDBC
Description:Office ...
Microsoft (R) Windows Script Host Version 10.0
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---Processing--------------------------
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ERROR CODE: 0xC004E016
ERROR DESCRIPTION: The Software Licensing Service reported that the product key is invalid.
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---Exiting-----------------------------