That is exactly the problem: you need to use PIO to constantly read the pins, and analyze the bitstream in software. At high speeds this takes up a substantial fraction of your compute resources, and it makes any kind of sleep impossible.
On a STM32 you can just set up the timer and forget about it until you get a "hey, we saw a pulse at cycle 1234" interrupt. The two are not the same.
My argument wasn't "this is completely impossible", but "this is needlessly complicated".
is 2.5ns (https://github.com/gusmanb/logicanalyzer) to 3.3ns (https://github.com/schlae/pico-dram-tester) resolution not enough for you?