The glitch has already been done at this point. You cant access hekate or no sd screen without glitching in.
So, again, take the SD card out of the equation 1st, minimize what COULD be wrong. FW of the pico shouldn't matter if you're getting 'no sd'. Only thing I remember that pico FW could mess up is something about boot0\1, I've never had to fix this issue though.
One second you say update the sd files and the next you say that pico fw can have an effect, and agree\disagree, or something...? I just don't want any more confusing info out there than there already is.
@nqtal, what happens if you press volume - and + at the 'no sd' screen?
Edit: Also, which version Switch is this again?
Edit2: Which version PicoFly FW are you using? Use picoflytoolbox to find out