Don't get too excited by the title of this post. The short answer to the question is, I don't know for sure, but probably not much. Nevertheless, I do have a couple thoughts here that may or may not be correct.
First, I suspect the Biden administration will look at the midterm results and think to themselves, "Our economic policy in general, and trade policy in particular, held up pretty well under voter scrutiny. Let's keep doing what we have been doing!"
My own view is that actually the midterm results were positive for Democrats for very different reasons than economic policy, most notably the Supreme Court's Dobbs ruling and the GOP putting forward some terrible candidates. But I can see why the Biden administration folks would come to the above-mentioned conclusion, and therefore I don't expect then to make big changes in trade policy. The IPEF, the TTC, etc. will go forward; the Section 301 tariffs will be reviewed as required by statute, but there will be no big changes to the U.S.-China trade relationship; and WTO reform will meander along.
Second, with regard to Congress, just focusing on the Senate races that could have a particular impact on trade, I think we are in about the same place we were before, or at least the place we knew we were going to be given the retirements of Senators Pat Toomey and Rob Portman.
Toomey was a strong free trader, and any replacement was likely to be more protectionist. I'm not sure there was going to be much of a voting difference between Fetterman and Oz on this issue, although Fetterman may be more of a true believer in economic nationalism than Oz.
Portman was knowledgeable about trade, and previously had negotiated trade deals, but he had been more protectionist in recent years. I don't think there would have been much difference between Vance and Ryan here.
In Arizona, Mark Kelly winning over America Firster Blake Masters is fortunate for trade.
Still outstanding is the Georgia runoff, where Raphael Warnock would probably be more pro-trade than Trump-backed Herschel Walker.
I'm not sure about the House at this point, partly because there are too many races to consider, and partly because the counting is not done yet.
Did I miss anything here? Probably! Feel free to point it out in the comments.