Does this mean that players with larger hands are allowed more cards? Or is it an idealized "you can shuffle"?

In practice there is no strategic benefit of having more cards. There is one bad deck that uses more than 250 (to win with Battle of Wits). It arguably breaks the rule already.

This is an interesting rule, as it seems to provide an advantage to players on the basis on hand size.

It's not, pretty much all decks stick to the minimum required number because the more cards in your deck the less likely you are to see any particular card you want or need. To that end where they're available in the format many decks will run 'fetch lands' which search the deck for a particular type of land in order to thin out the remaining deck.

More cards is not seen as an advantage. There are a couple cases where you may want more cards, but usually up to about 75. It's about drawing the right cards, not just many, and more cards makes your deck less reliable, simply on the likelihood of drawing the card you want.

Unless you really really want a Battle of Wits deck (which is maybe tier 7) there is really no advantage and quite a bit of a disadvantage to running more than the minimum allowed number of cards.

For those who don't play Magic, this is on a scale where tier 1 decks are top decks, tier 2 decks are reasonable, tier 3 decks have serious weaknesses but are playable.