Enterprise already did much of the groundwork for the Babel type storyline and I think it was even in Season 4 that they went there explaning it's continued use in TOS.
But we didn't see much interaction between the various races after that even in the Enterprise novels, it was always on Earth in the Coalition chambers.
We never saw say, a group of Andorians and Tellerites assigned to an Earth ship to help install new technology or software in the early months of the war, or taking them not to Earth, but between two of their own colonies when their own ships weren't available etc.
We know the Vulcans remained out of the war for the longest time but not the average-joe Vulcan's individual responce to that, maybe someone on the Columbia crew was stationed on Vulcan for years and has friends there they correspond with often.
Trip and Archer were involved in the NX program and the Warp 5 Engine development, but there were a lot more than two people working on them, so people from both are going to be on Columbia keeping an eye on her reactor and engines, some new interesting faces with new anecdotes about the 30 year development process.
Enterprise visited many worlds and has not had time to go back to each, Columbia will be trailing behind in Enterprise's wake of fame or infamy, living up to the reputation of her sister ship, making their own name in galactic politics. So plenty of pressure on Hernandez there.
We also hear very little of Earth's nearest Coalition neighbour, Alpha Centarui, so visiting them and their world could be interesting. They are alien but closer to humans than most, stern and unusual people. Cochrane "retired" there for a few years before disappearing, so we can assume they've known humans for decades at this point and the shipyards there are helping build the NX ships.
I'll stop rambling now.