Well, now I am looking for recommendations for vendors

I am specifically interested in dwarf irises
I reticulata
Dwarf Bearded Irises
Dwarf Louisiana Irises
Dwarf Japanese Irises

I can find a place to put them with full sun or
dappled shade as we have several big pine trees
in the yard

Dwarf bearded iris gardens: Mid-America gardens, Winterberry Iris gardens, Aitkens gardens, Stout gardens at Dancing Tree, Sutton's gardens. You see you can gaze for a day. that is just a start.

For Iris reticulata and Dutch Iris, I would recommend Brent and Becky's.

Do dwarf japanese irises exist? Can anyone give examples of them?

No dwarf LA's or Japanese exist. At least not in the US. You would be potting regular sized one.

For LA's try Iris City Gardens in TN or Cindy's Louisiana Iris. Both links can be found in the Vendor list thread. JI's, try Mt. Pleasant Iris, Ensata Gardens, Cascadia Iris Gardens, Aitken's has both JI and LA. That will give you a start. There are more if needed.

no dwarf 'ji's' that i know of, willinator. however, they do have different heights. you might choose the shorter variety? most of the vendors list the iris heights, and description.