And the level of conflict may have varied during that period. The U.S. and Soviet space programs were developed while the two countries were involved in a lengthy cold war that included armed conflicts of varying intensity throughout the world. The space programs themselves were spurred in part by the competition between the U.S. and the Soviet Union to develop the technology.
Capable of interstellar travel means which: warp drive, high relativistic speeds ships or generation ships traveling at a small fraction of light speed?
Duane's Rihansu series are some of the best Trek novels ever written. You should read them at your earliest opportunity.
In the Duane version, the ships travel at very high percentages of light speed, experiencing significant time dilation en route to their destination.
But they still almost ended up having to be true generation ships by the time they got to the Eisn system. And might not have managed.
Speaking about warp capacity, there's a difference between having a technological capacity and acting on it. It's quite plausible to me that Vulcan retained warp capacity after its first interstellar era ended with the planet's near self-destruction, but that afterwards the planet was too concerned with rebuilding to do much with the technology.