I feel this as well. If I don't initiate anything, the friendship will die down since everyone else is "silent" and busy with their life. If I ask too much, I fear that I'm needy and might bother others.
For real. And then there is also the classic 'their lives are probably a bit better without my crappy presence in it, so it's only moral to leave them alone'.
This is one reason why my men’s group is so great. The leader is a good cheerleader, like a mom. I express something like this and he’s like “I like you. I get value from knowing you. Where do you think this idea came from that you’re a burden?” and then we dig into it and it actually works. I’ve had so many mind blowing shifts in how my mind feels to be in, and how that changes my thoughts. I feel way less like an intrusion than I did before.