sorry for my late reply, email notification on updates to this thread were delivered to my spam folder so I didn't see them write away.
I'm not sure if I was able to follow you all along. I see the question about my Android device: it's a Google Pixel 5 with Android 13 (Kernel version 4.19.261-g768ca1b2052f-ab... as of March 16th).
I also activated 'Allow high MTU' and kept hitting "wait" when Android's message of ANR was displayed until logcat stopped more or less.
Then I cleared logcat, turned off my bandle js and stopped Gadgetbrige app from within the app (Burger menu bottom entry). Logcat was quiet. I started my BangleJS (saw a message in logcat appearing), then started Gadgetbridge and then connected. I copy pasted it to an new Gist: https://gist.github.com/graphcon/3abe2d6f83c2ffe95c21a7013f8ae15b
I feat, it doesn't start from when I started my bangle as there might be a limit of displayed messages. Not sure if I can expand this. Please tell me, if it isn't enough, I will then look into it.
I then kept hitting "wait" when ANR message appeared, but it doesn't seem to change anything.
There were no private messages/notifications while recording this logcat.
Also, I don't have any calendar apps on my bangle, does it always pull my events?
I use Circles Clock https://github.com/espruino/BangleApps/tree/master/apps/circlesclock
I did the same again (turn off bangle, stop gadgetbridge, ...). My bangle showed some messages at the bottom like "fifo full". It's still running and logcat shows a lot of "writing to characteristic" messages. But I received some personal messages so I can't provide you the logcat this time.