The Sky Object has no option to tile or to change the U, V length, as it has no UV data, to begin with.
There are two ways, but one has the need to replace the Sky object with a large sphere.
The first example works photographically. This means that at the moment we change the distance to our subject and change the field of view, we create a different relationship to the context (here the Sky). Since the sky object is rather infinite than close, this will produce the effect of the magnifying eh background.
The second example replaced the Sky with a Sphere, a large sphere. Now we have UV data to work with.
Since the Length U, V, will “move” the image around, we need to counter this with the offset values.
I have made a screen capture to illustrate this effect, plus project files:
Please note that the second version will not reproduce the light a 360x180º HDRi typically produces, as it is either cropped or tiled. Often there is a suggestion to split HDRi (light) and HDRI background, but it produces a more complex set up.
You could also render the background in the right size (Focal length) without the foreground object and then use the rendered image on a background object.
You might need to place your HDRi into it.
All the best