Ellicott offers this neat summary -
Jordan overfloweth all the time of harvest — This is meant, not of wheat-harvest, but of the barley-harvest, as is manifest from their
keeping the passover at their first entrance, (Joshua 5:10,) which was
kept on the fourteenth day of the first month, when they were to bring
a sheaf of their first-fruits, which were of barley. So that this
harvest, in those hot countries, fell very early in the spring, when
rivers used to swell most; partly because of the rains which had
fallen all the winter, partly because of the snows which melted and
came into the rivers. And this time God chose that the miracle might
be more glorious, more amazing and terrible to the Canaanites; and
that the Israelites might be entertained at their first entrance with
plentiful and comfortable provisions.
Matthew Poole offers similar comments:
This is meant not of the wheat harvest, but of the barley harvest,
(which was before it, Ruth 1:22 2 Samuel 21:9) as is manifest from
their keeping of the passover at their first entrance, Joshua 5:10,
which feast was kept on the fourteenth day of their first month, when
they were to bring a sheaf of their first-fruits, Leviticus 23:10 Deu
16:9,10, which were of barley, as Josephus affirms, and is evident
from the thing itself. So that this harvest in those hot countries
fell very early in the spring, when rivers used to swell most, partly
because of the rains which have fallen all the winter, and partly
because of the snows, which then melt into water and come into the
rivers; for which reasons the same overflowing of water which is here
ascribed to Jordan, is by other authors ascribed to Euphrates, and
Tigris, and the Rhine, and Maine, &c.