Thank you for your question! As of right now, applying sensitivity labels to your files and emails in Outlook on your mobile device is currently not supported.
For more info - https://learn.microsoft.com/en-us/microsoft-365/compliance/sensitivity-labels-office-apps?view=o365-worldwide#sensitivity-label-capabilities-in-outlook
If you'd like this feature to be implemented, please feel free to leverage our User Voice forums for Office or Azure. I've also added the "office-outlook-itpro" tag to this thread so our Outlook experts can provide additional info, as needed.
Thank you for your time and patience throughout this issue.
Please remember to "Accept Answer" if any answer/reply helped, so that others in the community facing similar issues can easily find the solution.