This is a tough one! The responses so far have surprised me because Prodigy is doing better than I expected - not that I'm complaining!
Discovery - I don't talk about Disco much because there's no point in spreading negativity constantly. Suffice to say, I think it had a lot going for it, but it had a few significant flaws that prevented me from fully enjoying the show. I bailed at the start of season 4, but will finish the show off someday
Lower Decks - I feel bad for saying this, but I haven't been able to get into the show at all - the humour doesn't really work for me. I usually love wacky, zany scifi but it left me completely cold

. Something else I dislike but isn't as talked about is the animation style - you can do simplified, stylized animation and still make a nice animation (Steven Universe comes to mind), but the way LD is made is, IMHO, awfully crude and uninspiring.
SNW is an enormous amount of fun. The cast is likeable, there are a range of different episode styles from madcap farce to horror. It also has insanely good production design, I mean my goodness does it look great. I don't take it too seriously, but I like having a cool adventurous show to watch at the end of a long day. I am a little concerned that the show could slip into Flanderized characterisation on the basis of that season 3 clip, but nevertheless, SNW is a contender for the top spot.
Picard had an intriguing season 1, with lots to like and a few things to dislike, which isn't bad at all for a first season of a Star Trek show. Then, season two happened. Easily the worst season of Star Trek in the streaming era for me, and maybe in all of Trek. I heard that Covid disruption was a factor in this? Season 3 however, whilst not being groundbreaking, did at least keep me well entertained, and they stuck the landing at the end. PIC is mid ranking for me.
However, Prodigy clinches it: Somehow a show not targeted at me won me over. They delivered a two season arc that is well paced, exciting, and has a satisfying conclusion. The characters are good, and all of them develop over the course of the show, with nobody underutilised. The animation is unbelievable, considering they don't have Disney/Pixar budget levels to play with, and everything is designed brilliantly. As a Starship nerd, the USS Protostar is easily my favourite new ship. Prodigy, from top to bottom is, the most assured and consistently good show of the new Trek shows.
If I was going with my heart rather than my head, then SNW would be number one for me. But you asked about ranking on overall quality, so Prodigy, despite being a kids/family show, manages to succeed at being a kids/family show a little better than the other series do at being what they intended to be.
1 PRO
2 SNW
3 PIC
4 DIS
5 LDS