Instead of a rule in Outlook, try this:
Build a new flow in Power Automate as an Automated Cloud Flow with the trigger "When a new email arrives (V3)" and fill in the relevant information about your mailbox and the sender:
Then add an action "Post a card in a chat or channel" and fill in the relevant Teams information:
For the adaptive card body, I used the following to populate the card with the message subject, the sender, the timestamp it was received, and the message body:
{
"type": "AdaptiveCard",
"body": [
{
"type": "TextBlock",
"size": "Medium",
"weight": "Bolder",
"text": "@{triggerOutputs()?['body/subject']}"
},
{
"type": "ColumnSet",
"columns": [
{
"type": "Column",
"width": "auto"
},
{
"type": "Column",
"items": [
{
"type": "TextBlock",
"weight": "Bolder",
"text": "@{triggerOutputs()?['body/from']}",
"wrap": true
},
{
"type": "TextBlock",
"spacing": "None",
"text": "Received: @{triggerOutputs()?['body/receivedDateTime']}",
"isSubtle": true,
"wrap": true
}
],
"width": "stretch"
}
]
},
{
"type": "TextBlock",
"text": "@{triggerOutputs()?['body/body']}",
"wrap": true
}
],
"$schema": "http://adaptivecards.io/schemas/adaptive-card.json",
"version": "1.6"
}
This should do what you're looking for.