Depends on the pond.
This was my 30 gal pond, 10-12" deep. Kept mosquitofish, fed them once in awhile, water was added from the lawn sprinklers. I had a small pump that I ran sometimes for aesthetic reasons. Cleaned with a $3 minnow net. Ran for several years. Clearest, cleanest and one of the most fav ponds I ever ran.
Next to the 30 gal pond was a
7,600 gal pond made of 6 connected ponds. Low fish load, no filters of any kind on a permanent basis (lots of temp filters of many kinds used for testing). Single 900 GPH pump. Source water was high KH and GH so testing wasn't really a requirement, but always good to know.
When I was growing fry in a 50 gal pond I needed a air pump and a 100 GPH water pump, lots of food so a good bio filter that was tested for performance, good mechanical cleaning, water temp and parameters were tested almost daily and adjusted as needed. Very high fish load, very high equipment needs.
"What equipment do you consider a must for proper pond husbandry and why?" IMO is has to the human brain and a willingness to use the cognitive functions rather than relay only on subconscious (imagination, myth) parts. Subconscious is important, but being ruled strictly by that makes for a poor pond imo.