Approvals to shared mailbox

Depending on the requirements you may be able to write a flow that contains the approval step like below but I don't know if that meets your needs.

I would need a more descript outline of what you want to accomplish but I've created flows like below.

Employee X wants to request Time Off (Start and End days)
Employee X fills out a Microsoft Form containing 4 questions

          Time Off Type (Choice dropdown with Vacation, Personal Time Off, Bereavement, Medical)
          Start Day and Time
          End Day and Time
          Comments (An optional text field with an area for the employee to justify the request.)

In the case above you could use a Power Automate flow with the actions below to approve the vacation.

When a form is submitted
Get O365 Profile (Using the submitter email from the trigger to find the profile.)
Start and wait for an approval
        (This step can be sent to the manager dynamic content found in the office 365 get profile action assuming your organization has that information set up and well defined.)
Convert Time Zone (Formatted in your preferred format)
      (Approver Submission Time)
Condition - (If Approval Response is Yes)
If Yes
     Send an email to the employee stating {Time off Type from trigger form} was approved on {Convert Time Zone}
Convert Time Zone - Time Off Start Date

Convert Time Zone - Time Off End Date

Create an Event (x2) - (Outlook, Google Calendar, etc.) using the Convert Time Zone steps above and the Employee responses from the form such as Time Off Type in the Employee Calendar and Shared Email Calendar (Employee Time Off Calendar)

If No
     Send an email to the employee stating {Time off Type from trigger form} was rejected on {Convert Time Zone} with the reason {Approver Comments}.