my sole experience is with garlic planted right at the base of pole
beans. Both did, indeed, do poorly. I had the same beans planted in
poorer soil a yard away, and garlic planted in the same soil a yard
away that did well (beans) or better (garlic). No explanation other
than they are enemies, and it was very obvious: bulbs were 50% smaller,
and the bean plants were 4 ft instead of 7. This year I have 2.5 ft
between the onion row and the pole beans, and the garlic is somewhere
else. Koniwng the extent of bean roots, I think that will be enough.
Most plants are allelopathic, so it might be that the bulbs affect the
vines.

Good companionship might mean a number of things: one plant has shallow
roots, the other has a taproot (so they don't compete for nutrients).
One plant is a light feeder and another is a heavy feeder for a
particular nutrient. One plant repels the bugs of another plant. One
plant beneficially shades the other. One plant produces nitrogen for
the other. And finally, their rhizosphere (the roots) might produce
chemicals beneficial to the other one. I doubt that there are plants
that can really help beans, except for those that might repel beetles,
though beans will help a number of other plants.

What I would really like to know is if cabbage/broccoli and tomatoes
are friends or foes. Different websites list them as either. The
cabbage could use the shade in midsummer.