Hi @xellemang,
If you're planning to use the out of box Approvals with Power Automate, unfortunately there is currently no supported way to modify approval records outside of the standard user interfaces.
You would need to look at some other mechanism to do approvals (e.g. SharePoint list or Dataverse).
With regards to using an SMS service to send a message and receive a response, you could leverage Azure Communications Services SMS connector. Currently the connector only supports sending an SMS message, but you can leverage Azure Event Grid to subscribe to more events.
These events can trigger flows when a message is delivered, and then also when you receive a response and parse the approval text. You would need to keep track of the thread ID from when it's delivered to correlate with a response back.
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