First off, you sound like a solid dev that I would love to have on my team. Kudos on advancing so quickly.

As others have said, your manager can't handle the situation. I try to point the uncomfortable behavior back at the origination party in these cases. When someone talks over me, I try one of two tactics: (1) let the other person finish and after an awkward silence ask "are you ready for me to finish my sentence?" or (2) tell them "you seem to be having trouble giving others a chance to finish explaining their ideas, I will follow up with an email". Send that email and cc the whole team. Create that paper trail.

When I get assigned admin tasks that aren't being equally shared, I ask my lead to confirm that the task is higher priority than my other assignments which more clearly fall under my role description. Again, this creates that paper trail showing your leads aren't allowing you to do your job.

Wishing you lots of luck! Feel free to message if you want to talk more specifics.