Friend purchased sailing boat without boom. Can anyone if what type of boom might be for this type connection to mast ?


This is a tough one as there is not enough information. Imho that is not a mast boom connection - the correct term being gooseneck.
1 What is the yacht type and model
2 What are the mast dimensions - fore and aft and lateral widths.
Suggest you determine the mast scantlings - dimensions as in 2 above - and then contact All Yacht Spars to get a proper gooseneck to suit.
This company is absolutely top shelf.
allyachtspars.com.au/
www.canva.com/design/DAGCz7Mdz_A/qYrRlj4s0OOigwKPFgxGmA/edit
Then for the boom you can hopefully find a suitable length and strength one on Gumtree or Facebook - a new one will cost an arm and a leg.