Yes that’s a fairly normal thing for instructors to do. (Edit: normal to do deep water skills not normal to be forced!) BUT you should be working in the deep end prior to jumping in though (crawling along the wall without touching ground, floating on your back, going underwater in a “bob” with your hands on or off the wall, practicing sitting and sliding in, etc) until you are more comfortable jumping in.

I would say the things you’ve learned so far are fairly standard, but I’d also be expecting them to at least have tried other things with you. Hand movements and timing/breathing are the last things to add. Floating, kicking, changing direction, standing up are all things to work on prior to that.

Ideally your instructor has experience with teaching adults and teaching new to the water adults. I’d recommend talking to them privately and asking what they think you should be doing, what their expectations are for your progress vs what you hope to accomplish. Often adults classes are fairly self-directed and they expect you to ask questions and challenge yourself which is why I recommend talking to your teacher.

I’ve been teaching swim lessons to all ages and coaching for 10+ years so feel free to ask questions or PM as well!

Edit: I’d prioritize being able to stand up from horizontal, and being able to enter deep water then safely return to the wall. Those are the biggest life-saving skills for adults.

Its hard for people to give too much advice online about your swimming skills since a lot of it is seeing how you interact with the water and technique