I don't think this is an American English thing as much as it is a social media thing (unless it has a third meaning in American English I'm unaware of). I've never thought of it as slang before, but I think this is what you're seeing (correct me if I wrong). In my mind the slang meaning of "reach out" doesn't mean "contact" as much as it refers to contacting someone you haven't contacted in a long time. For example, if I look through the address book on my email server, I can see there are people I haven't talked to in years. Similarly, I have 'friends' on my Facebook page I haven't spoken to since high school. Facebook might prompt me to 'reach out' to those people I haven't talked to in a while. That could just be sending a message saying something like "Hey, we haven't spoken in ages. What have you been up to?" It's not reaching out to them on an emotional level, but it's not the same as simply just contacting them. I wouldn't reach out to someone I spoke to last week (unless it's in the emotional sense). If I'm doing something like organising a party, then reaching out to my friends would mean I'm contacting more than just the half a dozen or so friends I see every week - it implies I'm also contacting people I haven't seen in a while, or people I only see a few times a year.

Ugh, I hope that the general population of speakers don't actually think this is the meaning. In the emotional context, "reach out to someone" means exactly what you thought it meant - to try to connect with someone emotionally and spiritually, usually through a difficult time. Among friends, it's common to "reach out" to a person going through a difficult time to try to help them through it. Sometimes, even strangers would do the same. During times of disaster or crisis (natural disasters or manmade), strangers will reach out to help those in need by offering homes, medical support, supplies, etc. Other times, it can mean "reaching out" to a person with whom you haven't had contact in a period of time to make sure that everything is okay. I was trying to figure out if the person "clicking" on the webpage should classify their actions more as a "ball is in your court" way. As in, the person clicking on the webpage took action, so now it's time for the other person to respond. Depending on the circumstances, it's possible they mean that? Ie. Person A said they were going to attend a function only if Person B attends, but Person B doubts the truth of that statement. Person B RSVPs to attend the event and, now, the "ball is in Person A's Court" to see if they will follow through on their promise.

I started to notice this in the 1990s, roughly. Business seems to be the biggest user of 'reaching out' in this context. I also see political groups, politicians and even the police use it in this way. Come to think of it, there may not be a group or individual who hasn't spoken this at some point. In fact it could be said that you have just reached out to the users of this group for their opinions. Su.Ki, did a question here start you to thinking about this? I remember seeing this phrase in an answer that you weighed in on a few days ago and at the time it struck me what you thought of the matter.

I use "reach out" to mean "attempt to contact." It doesn't have to be about anything deep or meaningful. I don't even actually have to talk to them, I just have to try to do so. In fact, I'm most likely to "reach out" to someone at work about a work detail (not even an important work thin, but something tiny). As a side note, when I really think about the phrase "reach out," I associate it with commercials (example here: https://www.youtube.com/watch?v=HO17B-ACRn0) that told us that it was ok to spend money on frivolous long distance calls. It's possible that AT&T is to blame for "reach out" being used in a mundane way.