The answer should be set PerformanceGoal -> "Quality". Otherwise PerformanceGoal options is set to global $PerformanceGoal which switches to "Speed" if the evaluation is done on a preemptive link. (default for most of gui/Dynamic etc).

See more in linked duplicate.

However, there appears to be a bug in 11+ which makes this option being ignored, fortunately Mathematica is great in workingaround bugs it introduces. So instead using the option we can Block the $PerformanceGoal:

Animate[
    Block[{$PerformanceGoal = "Quality"}
      ,  Plot3D[Sin[t x y], {x, -3, 3}, {y, -3, 3}, PlotRange -> {0, 1.2}]
    ]
  , {t, 0, 2}
  , AnimationRunning -> False
  , DisplayAllSteps -> True

]

The answer should be set PerformanceGoal -> "Quality". Otherwise PerformanceGoal options is set to global $PerformanceGoal which switches to "Speed" if the evaluation is done on a preemptive link. (default for most of gui/Dynamic etc).

See more in linked duplicate.

However, there appears to be a bug in 11+ which makes this option being ignored, fortunately Mathematica is great in workingaround bugs it introduces. So instead using the option we can Block the $PerformanceGoal:

Animate[
    Block[{$PerformanceGoal = "Quality"}
      ,  Plot3D[Sin[t x y], {x, -3, 3}, {y, -3, 3}, PlotRange -> {0, 1.2}]
    ]
  , {t, 0, 2}
  , AnimationRunning -> False
  , DisplayAllSteps -> True

]