Click the buttons one at a time in Edge. Note whether each one opens Teams, prompts then opens, prompts then does nothing, or does nothing.
msteams:/
msteams://
Message link - msteams:/l/message
msteams:/l/message/19%3Aeec99585f76544bd81ec095526bff462%40thread.tacv2/1783622701761?groupId=50df9aed-84da-44d6-9252-47604857a874&tenantId=bc810ed6-edba-427f-a0fd-8fdc9b90ab7b&createdTime=1783622701761&parentMessageId=1783622701761
Message link - msteams://teams.microsoft.com/l/message
msteams://teams.microsoft.com/l/message/19%3Aeec99585f76544bd81ec095526bff462%40thread.tacv2/1783622701761?groupId=50df9aed-84da-44d6-9252-47604857a874&tenantId=bc810ed6-edba-427f-a0fd-8fdc9b90ab7b&createdTime=1783622701761&parentMessageId=1783622701761
Browser fallback - https://teams.microsoft.com/l/message
https://teams.microsoft.com/l/message/19%3Aeec99585f76544bd81ec095526bff462%40thread.tacv2/1783622701761?groupId=50df9aed-84da-44d6-9252-47604857a874&tenantId=bc810ed6-edba-427f-a0fd-8fdc9b90ab7b&createdTime=1783622701761&parentMessageId=1783622701761