Why does Humanae Vitae not mention involuntary celibates/singles?

To answer the first question, I don't think the choice to leave out single people in a document about marriage was unfair. Humane Vitae necissarily leaves out a large number of people, including people who are divorced, widowed, same-sex attracted, single-parents, consecrated religious, etc, just because they aren't the focus of the encyclical. I agree that the Church could say more about a lot of people, but that's another conversation.

In response to your comment about marriage being a "choice of free will", remember marriage is two people freely choosing to be together. It is not the choice of one person, because that wouldn't be marriage. Even if someone really, really wanted to get married, they couldn't just will a vocation to marriage. The vocation to marriage is not being called to an abstract idea, it is being called to a particular person, a particular person who feels the same call and also wants to be married. Unless you meet that person, you can't make a free will choice to get married. Not being married might be frustrating because it's not your choice, but not everyone gets the vocation they want. There were plenty of saints who wanted one vocation and got another, so you have a lot of heavenly friends to turn to.

Edit/Re: what if no one by free will chooses to even give you a chance to win their heart (date, or court)? –

On one level, the answer is simple. If no one chooses to date you, then it probably means that, at least for now, you are called to singleness. I'm sorry if that sounds harsh or anything; I don't mean it as a put-down.

How you view singleness is completely up to you. It doesn't have to be seen as a bad thing. It doesn't mean that you are unlikeable, ugly, unworthy, defective or a bad person. It literally only means that you aren't in a romantic relationship. There are millions of factors at play; you don't have 100% control here.

People say no for all kinds of reasons. It might seem like they "aren't giving you a chance" or are rejecting you unfairly, but that isn't always the case. Maybe the person is interested in someone else or feels like they are called to religious life. Maybe they are other impediments to a potential relationship that they are aware of, but you aren't. A lot of times people aren't saying no to be mean, it's just that they don't want to hurt you by pretending that they want to be in a romantic relationship with you when they actually don't. Sure, some people in the world are actually mean, and genuinely like putting people down. But not everyone is like that, and you'll be much happier if you appreciate honesty.

Finally, it's not true that no one is offering you their heart. If you are Catholic and believe in the Eucharist, you know God literally is freely offering His heart and His whole life to you in the Mass/Eucharistic adoration, hoping you'll say yes and give Him a chance. I'm not a spiritual director, just a random person on the internet with zero credibility, but I'd be presumptuous enough to guess that God cares more about your well-being than you do, and that He cares more about whether or not you'll be a saint than whether or not you'll get married. Maybe, just maybe, He's letting you be single so you have a chance to find out how much you're loved by Him, instead of being completely distracted with trying to substitute it with human love.

Maybe try spending more time with Him. Focus on friends and family. Try offering your talents and time to others in service/volunteering. Spend time learning/enjoying life. That won't necessarily fix all the problems or find you a significant other, but you'll be happier with life as it is now.