I'm confused. Did all US and European airlines except United resume this route, or had other carriers in the US/Europe, like Austrian not resumed service in the war zone?

Often temporarily discontinued service for things such as missiles, volcanos, pandemics...they may not have a solid schedule on day 1, they may plan to operate and decide not to. The world is an uncertain place, and airplanes flying thru recently active trajectories of 300+ missiles with a likely retaliation in the near future, certainly qualifies as uncertain at best. Google "Malaysia 17" for the uncertainty of routes even considered safe. KAL 007 is another "safe" example, although not a direct comparison

If you look at the increase of commercial long haul flights in the past 90 years, the increase in power and effectiveness of missiles, then look at this list and notice how the number of aircraft shot down has DROPPED by magnitudes, when based on the 1st 2 fact, they should have increased. This is why they have been reduced. Carriers don't fly into danger and they avoid it for periods of uncertainty List of airliner shootdown incidents - Wikipedia

Transoceanic scheduling takes more time to develop, than say regional flying, so to resume service on a route with a 10 hour flight after an uncertain period of missiles, well, it takes longer (a to get there) to schedule (pilots, airframes...) and b) it's far more costly to divert for both passengers and carriers. So a carrier based in Cairo will likely fly before some US flagged carriers