Poor dude. It does seem like he's reliving his own trauma a little bit

(The other option is that he's doing this coz your focus is elsewhere and meowing is a way of getting attention from you)
I have my own visiting me and meowing at me - mostly coz there is a door between us, but also because she's no fan of water. I personally took a couple of moments to just...'demystify' the shower, and take her with me in there, turning on the shower facing away from her. That was enough to convince her that clearly I wanted to be there, but she didn't have to be
I personally, in your position, would take him in there several times a day, show him the shower, without getting him wet (and potentially showering your hand to show that the water doesn't hurt you), and take some treats with. That way you can show him that the shower doesn't have to be a miserable place. I'd also ignore him when he's bawling out there and you really are taking your shower, coz talking to him will keep him going, though it's certainly not a bad idea to do a training session right before, or right after your shower, just integrating it into your routine, as such. Again, it will also address the potential second option for why he is doing this.
That said, this stuff does take up precious time, so I'd get if you were not willing to go that far. But, ime, if you cannot distract them from their fear, the only way to go is to introduce them to it in a positive way and make them re-assess
Caveat:
assess his true level of fear when you approach the shower and stop if he becomes clearly upset, and start from the place where he doesn't flee yet, but clearly is focused on the shower. I'm not in a position to gauge his fear response from here, but you don't want to retraumatize him by taking him into the shower if that actually makes him utterly upset. Mine was unsettled, but she trusts me to such a degree that as long as I'm there, she'll tolerate an uncomfortable position - and then I adjust for her comfort level, if need be, once we're in that situation.
Fears typically are addressed by starting at that place where they're uncomfortable but not yet fleeing (so they can still learn and aren't stuck in flight or fight yet), making it a positive experience if at all possible and then gradually closing the gap between them and the object they fear, always using that 'out of comfort zone but not flight/fight' as a standard for when to stop and when to proceed.