My building's area has seen particularly heavy rains last 2 days, and
some water ingressed the building drom the side (not through the
roof).

The reason is that water level outside was too high.

There is a storm sewer in the back yard of the building.

Am I correct in thinking that the proper way to address this is to
hire someone to dig a drainage ditch along the property, draining into
that storm sewer, or into sumps inside the building (to be pumped into
the same storm sewer).

If so, what kind of companies should I look up in Yellow pages, what
is that kind of business called?

Thanks

i