However, when you squeeze your chest up to set your back, you should absolutely be supporting a significant portion of the bar’s weight in your hands. If it’s a 400 lb deadlift, you might now be applying 100 lb, 200 lb, maybe 300 lb of upward pull at this point. The specific numbers aren’t important (and they’re made up in this example, anyway) - the point is that you should feel significant weight in your hands because your hands are now supporting that weight (and correspondingly, the floor is supporting less of that weight).
Bonus Tip: Squeeze the bar off the floor.
Some lifters will do a good job of setting their backs with proper tension on the bar, and then they’ll make the mistake of slightly releasing that tension and then trying to yank the bar off the floor. This is usually a subconscious effort to get a bit of “down-up” movement out of the lift akin to the bounce you see at the bottom of the squat.