Why is opamp slew rate specified at unity gain?
Are the opamps which have a slew rate that varies with gain?


Generally an op-amp's slew rate is a limitation of the op-amp in being able to change it's output in one direction or the other for a step input change. It isn't affected by gain but it can be easier to mistake reduced bandwidth for slew rate limitation when measuring with a significant gain.

Remember that in pretty much all normal op-amps gain x bandwidth is largely a constant value so trying to measure slew rate with a big gain can lead to a false measurement if you are not careful.