The importance of proper breathing only becomes really obvious if you are diving deep maybe over 120or 140ft or if you are working hard. If you are relaxed and warm and floating around on a casual site seeing dive then breathing technique is not important.
I have found that a slower, cycle and a much more co.plete exhalation is the most efficient pattern. You got to remember to exhale all the way before starting to inhale. ,, Within reason of course.
Breath slow and deep and try not to move more than is needed, pull your self on bottom rather than kick and if you do get a little winded, stop and rest before continuing will help to conserve air.
I normally have a large enough tank that time rather than has supply is the limiting factor. Trying too hard to conserve air causes anxiety and can cause co2 headaches and is unwise and dangerous. The goal should be to remain calm and relaxed and the resulting air use should be good. Trying to force the issue by restricting breathing is NOT the way to generate calmness.
If you can act calm and relaxed, then your breathing pattern will reflect that and soon you will feel calm. The exact opposite of a fast, shallow,panting pattern. The feedback from your breathing pattern to your mental state is strong.