My guess on no Xbox trailer at the TGA is simply that they couldn't because it would actually harm them.
IMO MS have been trying for the past 18 months to transition from showing projects way to early (which they were force to do to generate hype for their new system release) to showing projects much closer to release. This obviously create a big gap where it is difficult to make new announcement or else the early announcement cycle continue.
Still they could have shown new trailer/gameplay video already announced titles but not really at the same time, the problem is those titles are either 2024+ or already have been their focus of past events. MS certainly don't want their 2023 projects to look like it's all they have when other actors are actually announcing new title for 2023, especially when 2 of 2023 most awaited titles ( which most likely would have been MS focus at TGA) have just been acquired.
This would have resulted in a spike in the kind of discussion MS want to tone down in the light of the merger reviews.