Were the English and Welsh longbowmen that fought at Azincourt, Crecy and other battles of the Medieval period as lethal and efficient as we are told? Were there any other groups of archers from other countries that had a similar reputation?

I don't know how we could quantify and compare reputations, but certainly throughout history many different soldiers/warriors enjoyed reputations as formidable/dangerous bowmen.

Earliest sourced example I can think of is that Herodotus mentions that prior to the Greek-Persian wars, it was a widespread opinion among the Greeks that Persian archery was formidable, and that no army could withstand the firepower of their bowmen.

During the period of the Punic Wars, Balearic slingers seem to have achieved some fame as excellent missile troops.

Later on, Mongol horse archers are of course, widely regarded as very successful and effective. But probably any of these horse riding nomadic/migratory peoples who employed Asian style recurve composite bows on horseback would have been regarded as dangerous opponents by foes from sedentary agricultural cultures, because they could only match such enemies capabilities with difficulty, with expensive and time consuming training. So again the Persians (Parthians of "parting shot" fame), but also Huns (who seem to have been at least partly behind the Eastern Roman empire's shift away from traditional infantry based armies towards a cavalry centered force that could match such nomadic cavalry tactically and operationally - source on this point is Grand Strategy of the Byzantine Empire by Luttwak), Turks, Avars, Khitans, etc.