What should I apply to seal the edges from leaking and seal the top from absorbing? Indoor use, subject to humidity.
Technically you don't have to do anything to it, many people have MDF benchtops with no finish on them. The moisture in the air is basically a non-issue for MDF, it's only liquid water that you need to be concerned with.
On a separate durability issue however, the edges of MDF are fairly friable and prone to damage. If you're OK with your bench taking its licks and showing it that's fine, use it as-is. But many people edge their MDF benchtops with strips of wood (hardwood or softwood, your preference):
As I think you can see the MDF in these benches appears to be without a finish.
In addition to adding durability to knocks and scrapes solid wood edging strips effectively cover the cut edges of the MDF and hence add quite a bit of water-resistance at the same time.
If you do expect you'll spill water on the bench then it is a good idea to apply a finish. Many people use a traditional workbench finish: a couple of coats of oil (usually BLO or tung oil), but you'll be better off if you use varnish as it is far more waterproofing (and the MDF far more prone to damage from water than the traditional solid wood).
Dilute at least the first couple of coats of your varnish by about 1:1 with added spirits to improve penetration, then two full-strength coats if you want very high levels of water-resistance.