Zero work is performed by a force on an object if

The work done by a force on an object is defined as $W = \int \vec{F} \cdot d\vec{r}$, where $d\vec{r}$ is the displacement of the material point of the object at which the force acts.

If the force is perpendicular to the acceleration, it is not necessarily perpendicular to the velocity. For instance, a force acting on a particle moving with a velocity that has components both parallel and perpendicular to the force can still do work, even if the net acceleration is purely perpendicular to the force. Hence, work is not guaranteed to be zero in this case.

If the force remains perpendicular to the velocity at all times, the instantaneous power delivered is $P = \vec{F} \cdot \vec{v} = 0$. Since work is the integral of power over time, the work performed is exactly zero.

If the object moves such that the point of application of the force remains stationary, the displacement of the specific material point where the force acts is zero ($d\vec{r} = 0$). A common example is the normal force exerted by a fixed hinge on a swinging door. Since there is no displacement of the point of application, the work done is zero.

If the object remains strictly stationary, all of its material points are at rest. Even if the spatial point of application of the force moves along the object (for example, kinetic friction acting on a fixed floor when a block slides over it), the displacement of any material point of the object is zero. Thus, $d\vec{r} = 0$ and the mechanical work done on the object is zero.