>As an admin, I want to remove some contacts in the contact folder of multiple users in my organization with one execution.
You won't be able to do it with one execution with EWS (or the Graph) it needs to be done mailbox by mailbox as that's the context you would be working in
before you go do the scripting route i would first try a compliance Search https://learn.microsoft.com/en-us/microsoft-365/compliance/search-for-and-delete-messages-in-your-organization?view=o365-worldwide#:~:text=You%20can%20create%20the%20search,Purge%20command%20in%20Step%203.
Eg using KQL like
kind:contacts AND EmailAddress:blah@keyman .com
should limit it to contacts that you can then purge but make sure you test it fully first to ensure you don't delete something unexpected.
otherwise if you want to start looking at EWS something like https://www.powershellgallery.com/packages/ExchangeContacts/126.96.36.199/Content/functions%5Ccontacts%5CRemove-EXCContact.ps1 may help but will requires the granted of explicit rights or EWS impersonation as being an Admin will have no affect when your working with any of the Mailbox API's