Session level back off?

Is there any way to signal that that the session is currently unable to handle a request but will be shortly?

Ideally I think I’d like something along the lines of Retry at this point in time, with an optional message and optionally informing which MsgSeqNum was last handled/accepted.

My use-case is that I’d want to prevent queues from filling up too quick, or to let an overloaded server get a short breather so that it can catch up.

Yes, FIX has a component to inform a requester that messages may be queued or throttled. ThrottleResponse tells the current status and may be sent in ExecutionReport and other messages. Additionally, rate limits and the action if a rate is exceeded may be published in advance using ThrottleParamsGrp in the UserNotification message.

Take a look at the FIX concept of message throttling, introduced with EP116 (https://www.fixtrading.org/packages/ep116/) back in 2010.