I don't know if the original poster replied in private messages but I also have these annoying purple arrow bubbles (PAB's) and wanted to provide some information based on your questions above.
I'm using Microsoft 365 Apps for Business.
Version 2406 (Build 17726.20160 Click-to-Run) (I ran the check for updates wizard and this is the latest version available to me)
The events that seem to cause these PAB's have this in common:
-All day events which span several days
-Show As status is Out of Office
-The do not have an recurrence schedule set
The PAB does not appear on single day all day events where the Show As status is Out of Office
The PAB's only started appearing on appointments in my work based outlook calendar from March 2024 and have not affected my personal outlook calendar which is also set up within the same Outlook desktop app.
When I originally set an appointment status to Out of Office, the PAB's do not immediately appear.
When I close and re-open Outlook, the PAB's now appear.
When I delete an appointment that has the PAB's the PAB's do not immediately disappear.
When I close and re-open Outlook, the PAB's are still there. (Note I am not doing this over time. I am closing Outlook, waiting for the process to close in the task manager and relaunching Outlook)
When I close Outlook by using End Task using the Task Manager, the PAB's disappear.
I also checked the web-app for Outlook and the PAB's do not appear. The web-app is not sufficient for me to work in daily and not a viable replacement.
When I switch the desktop version of Outlook to New Outlook, the PAB's do not appear. As with the web-app version of Outlook, this is not a viable replacement. It is clunky, the view is not compact enough, the layout is not as flexible as the desktop app so I will not switch to New Outlook.
I cannot click on the PAB's and no pop-up, help text appears that gives any indication what the purpose is.
I hope this is enough further detail to help you find the cause of this annoyance and a way to remove it as it detracts from the calendar date and is completely and utterly pointless unless there's some reason that I am not aware of.