Yep, your puppy is a genius at their foundation tricks in the living room. They are so good, they are making you nuts. Keep working on them.
Keep revisiting these games and incorporating these foundation behaviors as much as you can in as many places as you can. The more you work your foundation, the more the things that are built on top of it stay strong.
The list of foundation behaviors is long and takes a long time to work through. As your darling puppy gets older and more independent, you might find things change a bit so keep cycling back to the basics periodically, especially recalls and attention/focus games.
Also notice that typical training classes emphasize a lot of treats, so keep the reward system as strong and variable as you can. Most puppies readily play with their owners and after one 6 week puppy class, most puppies have learned to expect treats and are reluctant to play - only because they have learned to expect a cookie.
Building these behaviors so they are very strong in lots of situations is simply a matter of playing these games in lots of situations with lots of tiny variations.
Think about each behavior as a question you ask your puppy: “Can you X, if Y is happening?” Allow your puppy to answer yes or no and then learn from their response where to go next with your training.
Caution: many people fast forward to what I consider first floor behaviors and skip some of these basics. Doing so, will limit the options that you have for training agility behaviors which may ultimately impact how well your dog learns them and how well they can perform them long term.
Converserly, a strong foundation is a proven way to make training obstacles, competition mindset, and response to handling much easier for you and your dog, and produces better results.