Also, the fact Fangmei hides her sadness is still ultimately a foil to Ryo, who doesn't know what to do with his sadness. The entire point, I feel, is to show how many characters react to sadness and loneliness to contrast with Ryo and the many paths he can take. Ine-san deals with her depression by cleaning all day and making sure the Hazuki residence operates as Iwao wished it. Fuku deals with his depression by funneling his sadness into his martial arts and practicing everyday to be the student Iwao wished him to be. Fangmei lost her parents and was placed in an orphanage. She honors the caretaker that adopted her every day by showing her gratitude to her temple and her faith. Wong and Ren are also orphans; both turned to crime to deal with their lack of needs. Xiuying not only had her parents murdered, but she lost her brother as he was driven to revenge. Instead of lashing out and going with him, she turned to religion and martial arts as a manner of dealing with her demons. Shenhua never knew her original parents, and has a stepdad. She deals with life knowing the only way she knows how and is pretty happy. Lan Di let his anger stew for decades to exact his revenge. His father was murdered, and he turned to crime and martial arts.
Mostly every character of import has their own demons that are relatable to Ryo's struggle for vengeance. The important thing to grasp is that they've all gone in their own ways of handling death and sadness. Shenmue is a story about Ryo Hazuki and the "potential that could either destroy him or realize his will." Mostly every character is there as a foil to show THEY handle their own personal demons to help Ryo along his path.
Expect Ling Ling to be another foil
Ultimately, how Fangmei feels isn't important - it's what she DOES - that's important for Ryo to learn a lesson from.
Some interesting thoughts here - it's kind of intriguing, for me anyway, to look back on certain details of Shenmue's story now that I'm older, and pick up on things my teenage self wouldn't necessarily have understood/appreciated. The theme of losing your parents and how you choose to deal with it seems to be a major one, which as you say all of the orphaned characters in the game deal with it differently. While I've always thought the whole 'dating sim' aspect of the game with Fangmei is a bit weird/creepy (Ryo bonds more with a 14 year old than a school friend of his back in Japan who was the same age as him??), her role as a character is still important, as it shows despite losing her parents she has still been able to carry on and live her life, even if her cheerful nature is sometimes just putting on a brave face. You are quite right that she is intended to demonstrate to Ryo one of the many ways you can deal with loneliness and grief.