Office 365 room mailboxes CalendarProcessing access via Microsoft Graph

I don't see anything in the MS Graph Reference that would do what you want. With that said, the barriers you state in your question for using the remote powershell api shouldn't be hard to accomodate.

For starters, your IT provider for email should work with you to configure rooms the way that you want/need. If they are willing to delegate this to you, then there are ways to set up Role Based Access Control (https://4sysops.com/archives/create-custom-rbac-roles-in-exchange-and-office-365/) to give you only access to calendar processing.

Likewise, MS has posted instructions and tools to use MFA with Exchange Online Powershell (https://docs.microsoft.com/en-us/powershell/exchange/exchange-online/connect-to-exchange-online-powershell/mfa-connect-to-exchange-online-powershell?view=exchange-ps).

According to your description, I assume you want to get the subject of a meeting room.

There is no reference on official Doc for your case yet, we can post this issue to the Graph support on the User Voice.

The only interface I'm aware of for managing this (beyond the Exchange UI of course) is PowerShell.

This isn't supported by Microsoft Graph or Exchange Web Services. It's worth noting that even if this operation was supported, it would still require an Admin to execute it. Operations of this nature almost always require Admin Consent.