Have you played the rest of the series?

I did, and it's a good thing because CS4 and Reverie depend a lot on you having played both Zero/Azure and CS1-3. Not a lot of Sky connections on the recent games though, just a few returning characters.

And I want to play the whole series from start, so not playing any of the later games until I have finished Trails in the Sky 😀

I'm one of the renegades that don't think playing in order is truly necessary. Sky has only one plotline that gets carried into Zero/Azure and CS1-2 is mostly self-contained, so it's perfectly fine IMO to play these out of order. Yeah, you lose some references and gets some spoilers, but nothing that will ruin the fun from the older games if you play them later.

In fact, I believe I went Sky 1-2 -> CS 1-3 -> Sky 3 -> Zero/Azure -> CS4 -> Reverie, and the only time I truly felt "yeah, I should have played the earlier games first" was during the Crossbell section of CS3.

How are you enjoying the game?

The beginning was kinda mid because it starts with Lloyd's route in Crossbell and that part feels like we're just rethreading the plot of recent games, but gets much better once you open the other two routes. C's route being an all-new cast is really great in making the game feel "fresh", so much that I wish the game started with that one instead of having us go through the early sections of Lloyd's and Rean's route first.

It also has a very strong "Sky 3rd" feel, which is good because I think that game is really underrated. The Reverie Corridor is almost Phantasma 2.0, and each of the main routes seems more streamlined than the average game with this series, with less sidequesting and more focus on the main story.