Some weapons have the "versatile" property.
They can be used with one hand or both hands. It should also work with longswords, battle axe and warhammer.
They do more damage when used with both hands.
I know about "Versatile" (and am a bit miffed it can't be toggled like other features). But that's not what this post is about. It's about helping other users like me who, through experience with other similasr games, may have assumed that staves are two-handed.
But you don't get the full damage with one hand - the staff drops from 1d8 to 1d6. A longsword goes up from 1d8 (1H) to 1d10 (2H) but you obviously can't use a shield or off-hand weapon.
I'm never really taking staves for melee damage, but they still get Topple when used one-handed.
And as alluded to, what are the other options for Shillelagh in the game that provide the same bonuses as some of the better staves? You can theorise that clubs might do a better job than staves, but if clubs with equivalent bonuses don't exist in the game, that theorising means diddly-squat.