Sometimes that’s okay.
As long as it’s not overly one sided and they do engage when you message them, don’t overthink it.
If it’s really that one sided then it should just naturally fizzle out without much thought. Either way, it’s not worth worrying about.
This isn’t really a big deal. A lot of introverts are friends with extroverts because they’re more comfortable doing things they don’t want to do. It’s no different than being friends with someone because they work harder to maintain a line of communication. So long as you show appreciation for that dynamic it can be healthy, especially if you’re up front about your struggles.
Lots of extroverts would appreciate how they’re allowed to be the center of enertainment within the group or that they’re allowed to take the reigns on what the group does. So long as it’s symbiotic you’re needlessly dropping potentially amazing friends by overthinking and applying your version of fairness that probably doesn’t match anyone elses version. It’s far better to just put in the effort you want to put in and keep expectations at a minimum.
I’m autistic and i almost never remember to initiat the conversation, or feel like it’s not appropriate. If any of my friends felt like you do, i won’t have any more friends. And i love my friends a lot and can’t survive without them. Don’t over think it. Each has their own way of socializing. It’s about the journey, not its initiation :)
Who keeps track of that? Seems weak.
I see this on askreddit all the time, “I realized I was the one reaching out, so I decided to let them initiate the conversation. We haven’t talked in years”.