Update:
reading sections 17.4.12 and 17.4.7 of RM0456 (Rev 5), It's possible to have an external trigger for transfers, and configure the DMA to run a "recursive" linked list, meaning that the last entry points back to the first one. The GPDMA is configured in "run-to-completion" mode (GPDMA_CxCR.LSM =0), and that way the DMA transfer never "completes". You can continue sending external triggers indefinitely.
I'm not sure how you plan to use this, but it looks possible.
The Juggler's Solution:
The DMA peripheral is allowed to write to the memory-mapped registers of various peripherals on the chip. With the "bit-banding" support in STM32, you can also have DMA write to specific bits (*). Combine this with the Linked-List DMA functionality and, with some jiggery-pokery, you could probably arrange things as you wish.
It should be possible to craft a write-white-where primitive using any comms peripherals with these tools, as long as you have sufficient control over the external host in terms of on-the-wire protocol and wait states.
One possible way (I'm just speculating here) is to have:
wait for EXTIx -> EXTIx Edge->trigger DMA Ch1 -> ll1 (clear TC flag for DMA ch2) -> ll2...n (do tha thingz) -> DMA_CH1_TC event->Trigger DMA CH2-> (clear TC flag for DMA ch1) -> (da capo).
(*) as JW rightly points out, I was wrong. Bit-Banding is neither available on the STM32U5, nor is it usable with DMA on chips where it is available.