In some cases more onchain transactions does mean more rewards for miners, as transactions will need to outbid with more fees for blockspace. How this relates to hashrate depends on things like the ratio of the block reward vs the block fees.

But in the context of "what if the the whole world uses bitcoin", the vast majority of transactions will not be onchain. But instead will be transacted via other more efficient layers (sidechains - like Liquid, or level 2 - like lightning).