Xenosaga was supposed to be six games. Originally the story (spread by EGM and other magazines) was that it was a retelling of the six historical eras of Xenogears Perfect Works (meaning Xenosaga Episode 5 would be a remake of Xenogears). Turned out the magazines were pulling all of this out of their ass and Xenosaga was actually some sort of retelling of Xenogears Episode 1 (the 10,000 years ago "humans in space" part of Perfect Works). However since Square owned the rights to Xenogears, they couldn't even do this, so it was more of a "spiritual reimagining" of XG Ep 1, with a few things altered to avoid a lawsuit (for example Xenosaga Ep 3 takes place in 4548 T.C. while Xenogears Ep 1 takes place in 4547 T.C. so they can't be related please don't sue).
The first Xenosaga sold very well due to all the Xenogears fans turning up, thinking it was a prequel. When it turned out to not be, and was a fairly subpar game compared to XG, a lot of those fans tuned out. XS2 was pretty bad and at that point the only people still playing it were strictly Xenosaga fans from what I saw, who spent a lot of time making fun of Xenogears fans on online message boards for trying to draw connections between XS and XG (which is all people ever wanted). Then the XG people just noped out entirely and left the XS people to sit around wallowing in their cyborg-on-scientist fanservice or whatever the fuck they were into. Xenosaga 3 sold even more poorly, which is a shame because it's the best of the 3 games and contains a TON of Xenogears references and fanservice, finally. They wrapped the story up with XS3 because after XS2's sales it was clear that people weren't interested in the planned six-game series.
So to answer your question, yeah, Xenosaga ended with Ep 3 and wrapped everything up real quick in the third act, which is pretty much just a long line of boss fights with every unresolved bad guy (pretty clear most of it was supposed to be over 3 remaining games). You didn't miss much with XS2. It's one of the worst RPGs I've ever played in a gameplay sense. The story's good, the settings are actually pretty amazing and it's one of the more atmospheric games on the system. Buuuut they ruined it by having an almost-incomprehensible battle system where every battle could essentially be won by entering commands in a certain order to trigger things like stagger, and otherwise you were just kinda confused most of the time. XS3 is worth playing if you want to revisit Xeno on PS2. Mostly if you liked Xenogears, since XS3 is like one big Xenogears homage. Two games too late, but yeah.
As for Dragon Quest, I'd play 1-3 in their original-ish forms (their SNES versions are as late as I'd go) before the remakes. Their original forms are full of surprises that'll largely be spoiled by the remakes. By the time the remakes drop you could easily play the majority of the series. The first 3 are all fairly short games and seeing their historical significance firsthand is a good time. Then later play the remakes in their (different) order. And yeah, DQ10 is inexplicably Japan-only, and an MMO. They made a single-player version of it that's more like the rest of the series, but didn't translate it or release it outside Japan because.... why? I have no goddamn clue.
I think someone's doing a translated Switch ROM of the single-player version of DQ10 and if that sees the light of day it's gonna rocket to the top of my list of things to play.
Another note on Xenosaga. It's got some insane music. Fatal Fight comes to mind (one of the final boss themes in XS3)
