Is a young man's grooming of his beard and his pride in it, on the basis that it is an adornment for men and increases their beauty and manliness, considered hypocrisy (riya’)?

It appears that what you mentioned is admiration, not showing off (riya'). Admiration has three detailed cases in Fatwa no. 68766. You can also refer to Fatwa no. 161841 regarding the ruling on trimming the beard, and Fatwa no. 35245 to understand the reality and types of riya'.