Looks like I haven't played since version 1.0.5 and now I downloaded 1.0.7. Is there a great deal of difference to really dig through a new run of the game or is it more smaller quality of life updates? And if it's okay to drop this question here too, how are future releases for new chapters or updates looking at this time?
I do a dev log for each new release, and clearly label them, so if you're every curious you can just thumb through those. Since you asked though: It looks 1.0.6 changed data crystal handling, which will be important to carry your info over to Chapter 3. At the very least, you'll want to carry your normal saves over to an updated version of GT and play through to whatever ending/playthrough you want to be "official", so that the proper new datacrystal is written to the game directory (you can check the "created" date on the datacrystal file to make sure it's fresh).
1.0.6 also updated the lighting engine to run better, and added a load option to the menu, but those are obviously QOL, not crucial. 1.0.7 just fixed a sprite glitch in the gallery, so again, minor. Long story short though, I still would recommend getting the newest version and genning those datacrystal file(s) in prep for Chapter 3.
As for how 3 is going, again, I post an update to the dev logs here every three months or so, next one is planned at the end of this month. Currently nearing the end of the programming/game design for the game(for initial release) (hopefully also by end of next month), which will "only" leave drawing, writing, and slotting in the planned scenes, which I estimate at 4-5 months.