In Iran, there's a social custom regarding "getting a haircut" i.e. whenever a man/boy gets a haircut, people congratulate him on the matter: In Farsi, we say: "Mubarak"! Is there an English statement, expression or saying for this case in American or British English? if yes what is it? I wonder if we can say:"Nice haircut"! I have never heard English speaking people saying" Congrats" or "Congratulations", am I right?
No, there's nothing that matches that cultural behavior where you're expected to say something no noticing a new haircut.
It is up to the speaker to choose to say something and more often than not, nothing is said. One might say 'nice haircut!' or 'looking good!'.
'Congratulations on the haircut' would sound terribly formal, like your butler said it, and 'congratulations' all by itself would be strange, everybody wondering "what he is being congratulated for, I mean it's obvious he got a haircut but why is he being congratulated for it, did he win it in a lottery? It's not like he's getting married or having a kid."
By expectation, I mean something similar to 'bless you': when someone sneezes, someone is expected to say it, and if no one does it seems like something is wrong.
Congratulations is used when there is an unusual achievement, like engagement, marriage, graduation etc. Using it on a regular activity does not sound good. Just "nice haircut" or "like it" is okey.
By the way, as far as I see, Arab, Farsi and Turkish people use specific terms after a clean shave or haircut (Na'eeman in Arabic, Sihhatler Olsun in Turkish), which could indicate such tradition belongs Eastern cultures.