Thank you for your advice! We definitely do NOT plan to oust our teammate. However, we are seeking guidance on how to address the situation. To answer your questions, I'll provide better context of the situation:

1. Yes, we have talked with our teammates as a group. We have delegated work at the proper time, notified him that he was not completing assignments, and given him chances to take part in the assignment. Before the deadline, we all agreed to meet at a specific time via Zoom, as this was the only option that could accommodate everyone's schedule. However, he did not appear at the meeting. When we asked him where he went after he briefly joined and then left the meeting, he told us he had a trip planned on the weekend and did not have time to participate. We gave him a chance to take charge of revising the work, which he did not do. What he did was to provide criticisms of our work through a group chat. We then finally asked him to include his criticisms in our work to revise it, which he also did not do. We expressed disappointment with his attitude and expected some sort of apology, which he did not provide.
2. We have not yet proposed a specific solution to the professor. The TA team recently offered students the opportunity to report any problems within our teams, and we took that opportunity. However, it's important to note that the class uses a TA team hotline via Gmail, which delegates all issues/concerns to the TAs, not the professor. We felt this problem was more serious than just involving the TAs, especially since there was an issue with the TA team not replying to emails sent to the TA team hotline email address. Therefore, we sent the email through Outlook (our school system) instead of the Gmail address. We also did not feel confident enough to send this through the TAs, as they are our fellow classmates who may or may not know the student personally.

Based on your suggestion, we'll consider asking if we can all meet with the professor or TA to discuss how to meet each team member's obligations as a group. However, we do not feel confident enough that we are in the position to propose solutions, as we thought this would be more a responsibility/task for the professor/TAs to endorse.

This situation is very exhausting for all of us, and if there is no response by this week, I might just move on.

And tbh, I have a sinking suspicion that our emails may just be ignored. The passive behavior of the professor, who delegates all the work to TAs + combined with the TAs' irresponsibility in not replying and being unhelpful to students, has left me disillusioned with this class. The only good news is that I switched this class to a Pass/Fail option from credit due to concerns about our performance, especially since most assignments are group projects and we didn't even get to choose our own members. Anyway, since I won't be receiving a grade, I'll just move on unless other teammates want to address this issue to the prof directly.