Sorry you havent heard anything from me for the past weeks.

Others have answered well and offered good suggestions for alternatives. Personally, as a young millennial American, I would use the term "ghosting" here. It matches perfectly with the meaning you're alluding here to, but is very colloquial and I wouldn't expect an older person to use it. "Sorry I've been ghosting you." "Sorry for ghosting. I'm so happy to see you again!" Ghosting is a term borrowed from digital communication when someone very suddenly or abruptly stops sending chats/texts/emails back to you and the conversation/contact is kind of left hanging. For instance, you might have met someone at an event, exchanged contact info and started chatting over text, gone on like that back and forth for a few weeks, and then all of a sudden never hear a thing back from them ever again. That's where the term "ghosting" comes from; it's like they disappeared and became a ghost. In a social context, it can be used whenever someone gets very busy or otherwise temporarily withdraws or "hibernates" or takes a break from their usual social activities or interactions. Hope that helps!

"Sorry for having disappeared for such a long time" is a sentence I have said numerous times. It is correct as-is, and implies exactly what you're saying-- that the individual speaking basically stopped interacting with, talking to, or seeing the person to which they're talking. Alternatives would be: Sorry I've been so busy! Sorry I've been gone so long. Sorry that I've been distant. And so on, however, each of these has it's own connotation or specific nuanced meaning, depending on the context of the lapse in communication/contact.

You can say. Sorry we didn't speak for a while. I was super busy. long time no see ...

There's nothing wrong with using the word "disappear" in this context, because it makes sense, but it is a little direct and in polite company it may make people uncomfortable. Instead people in a polite situation would say "I'm sorry for losing touch". In a super friendly situation, however, you might even hear someone say "Sorry for going AWOL" which is a military acronym for "Away With Out Leave".