The episode of shabbos at the Sin desert is not about melakha, it is about choq.
No mention of melakha is made in the episode's text. Quite the opposite, the manna was about the gift of grace from God. The manna was an exercise in defining deservedness, as the paschal lamb was an exercise of defining deservedness. Both measured the needs of the household.
The practice of collecting manna according the needs of the household accustomed each individual member of the Children of Israel to acquaint themselves with their various needs, more than which would have consituted excess. The manna allowed God to define the measure of sufficiency for each household. To attempt to collect an excess of what was sufficient was to no avail. Each household ended up only with what they deserved by right.
Nor could they store any excess. It would putrify overnight. (This putrefaction, hivish, recalls what happened to the fish and the frogs in the first two plagues of Egypt.)
Only the extra measure on shabbos would keep.
A mishmeret is a storage of surplus. A mishmeret does not hivish. The mishmeret extends to all the generations of Israelites, which is why Aharon kept a sample of manna as a standard against which future generations would measure how much was enough.
An omer is approximately half a gallon.