M2P DMA transfer with trigger from a different peripheral
DMA requests from each peripheral are hardwired to either DMA1 or DMA2, see the request mapping tables in the DMA functional description of the reference manual.

So a request from TIM1 or TIM8 can trigger a copy operation only in DMA2, other timers can only trigger DMA1.

While DMA2 transfers can reach any peripheral, the peripheral addresses on DMA1 are restricted to the APB1 bus.

A request from TIM8 can trigger a stream on DMA2, which is able to copy something to/from the registers of TIM3, but it doesn't work the other way round, because TIM3 can only trigger a stream on DMA1, which is not able to reach out to TIM8, which is on APB2. DMA1 can only access timers 2 to 7.