Watching through all the Arrowverse shows in chronological order (not quite airdate order, there's slight reordering all throughout to link all the crossovers up right) is a task that starts off reasonable, and then slowly reveals itself to be insane. It's doubly awful if you try doing it in Australia without a VPN, where all the shows are on different streaming services, except for Supergirl which is on none of them.
Still makes it weirdly satisfying to watch and see all the more minor crossover details turn up between shows that indicate you actually are seeing all this unfold in the right order. It also makes Arrow metatextually hilarious, because you can see the exact moment in season 2 where they decide what they want to do with The Flash and how they need to make Arrow a little more fantastical to have the two fit into the same world... and then realize when the first season of The Flash starts that they did not do enough because Arrow characters turning up in The Flash feels weird every time.
I got to Supergirl in this journey, and... ooh boy, this one hurts. Going through the other three shows on the way to it makes Supergirl all the more stark, because compared to all those other shows, Supergirl treats its protagonist like shit. There's a few notes that these sorts of serialized superhero shows apparently have to hit sometime, and Supergirl hits them way faster. The 'actually, maybe this superhero is bad' trope doesn't really get going in Arrow until a decent clip into the first season (and he's meant to be the really shady one so it should've come quick), and it doesn't hit The Flash until season 2, but Supergirl gets it in the second episode. The first time the hero fails because their skills aren't enough hit Arrow and The Flash at around the episode 6-ish mark; it happens to Supergirl in the pilot, and basically the whole rest of the episode is spent beating the shit out of her.
It's also kinda funny that it was supposed to be the higher-budget one of the lot in its first season, but looks and feels really cheap in comparison. A big part of that is just that Supergirl doesn't have as visually interesting a powerset (especially since we've had so many Superman movies), so the action scenes aren't as flashy with special effects or choreography, but there's more to it I can't quite put my finger on. The aliens and the black ops military stuff feel very 'early 00s', somehow.
Also also, the show's rogues' gallery just feels kinda sad. Supergirl doesn't really have much dedicated supporting cast or villains like Green Arrow and The Flash could build their shows around (and Arrow cheated by stealing Teen Titans stuff, so that's off the table, too), so especially early on it's working with some really cut-rate names.