Hi Özgür,
Thanks for the detailed screenshots.
For the problem showing in the first screenshot:
The date format of the "data entry part" is based on the computer's Region settings. In Windows, click on the Start, just type "region", click on the pop-up Region settings, you may change the setting of the Region format to the United Kingdom.
*I also suggest you change the setting of the Country or region to the United Kingdom.
**You may also click the Change data formats button to change the detailed settings of the Regional format data.
For the problem of "date format showing differently in Microsoft Teams".
In Microsoft Teams, you may click on the user picture -> Settings, on the General tab, change the Language to the United Kingdom. Save and restart Teams and check the result.
After confirming the problems disappeared in both the Excel client and Microsoft Teams, check whether the third problem persists after clicking the Open in Desktop App button on the navigation on Microsoft Teams.
Besides, I would like to suggest you refer to this article: Change your personal language and region settings. The Locale setting affects the date formats of Excel workbooks stored in SharePoint Online (after clicking the three dots ... -> Open in Browser on the upper right of the opening workbook screen in Microsoft Teams) and OneDrive for Business.
*The change may need up to 24-hours to take effect.
**I’m also testing to confirm that.
Hope this helps.
Just post back if you got any trouble during trying the suggestions. I also appreciate your patience as well. :)
Best Regards,
Hugo