To manually clear your application cache for Microsoft Outlook on the web:
Google Chrome (Mac)
Right click anywhere on the browser screen and select "Inspect"

On the right, a debug window will appear.
At the top you are looking for "Application" which might be under the extended menu (see the arrows).

Expand these three sections:
- Local storage
- Session storage
- Cookies

Under each of those you will see an entry for Microsoft Outlook. It will look something like "https://outlook.office..."
Starting at the top (which should be Local Storage), right-click on the https://outlook.office... entry and then choose "Clear".

When you click "Clear" the entries on the right should be deleted. A couple will start to appear again as the page refreshes itself and you might end up with only a few entries.
Your Microsoft Outlook web browser page should also sign out:

Before signing into Outlook again, you should do the same (right-click and clear) for the other two sections: Session Storage and Cookies.
Once you have done that, close that browser tab or window and then open a new one and visit https://office.com
You will need to sign in again - do so.
You can load Microsoft Outlook again by using the menu at top-left:

And finally, close the inspection window by using the cross at the top-right:

Microsoft Edge (Mac)