I'm trying to learn piano and music theory by myself but sometimes it's difficult to know what to learn and how to approach the topics, unfortunately getting a teacher is not an option for me.

I already learnt the major and minor scales on each key with both hands together, the major and minor triads without their inversions and how to recognize the keys on the staff.

Now I wanted to master the intervals, but what is there to learn about them? I already know the basics of what they are and the logic behind them and this is what I think I could learn:
-Recognizing them on the staff
-Recognizing them on the piano and being able to play them without thinking too much
-Recognizing them melodically on both directions by ear
-Recognizing them Harmonically by ear

Is there something else I should learn/practice related to the subject or something I should omit?