Well, singing lessons is a lot of doing simple exercises, like hearing some notes, and then try to sing those, or hearing a note and sing a third higher, for me atleast haha. Probably the same things you did while doing plays and practicing piano. The one-on-one is great to perfect your technique. I taught myself wrong, before I started but you probably wouldn't notice in a group, but with one-on-one you can notice and fix it within no time. I have a unconventional taste in music, so it also gives me the space to sing music I like instead of pop.
I love the timing most scat singers can put in their music, it really allows for that swing in your music, it really is great.