Apparently chests can be found
As Thomas Markov points out in their answer to this question, there is at least one published instance of 5e creatures going looking for chests. In Icewind Dale, there is
a coven of hags which "frequently leaves its den to roam the Ethereal Plane in search of treasure chests tucked away using the Leomund’s secret chest spell"
These creatures are Int 16 and Wis 14, so presumably if they are trying to find chests, it is reasonably possible to do so.
It is probably hidden in the Deep Ethereal
As described by the DMG, the Ethereal Plane is "mostly featureless" (p. 43), it "envelopes" the Prime Material in a great wheel (p.44), and is "a misty, fog-bound dimension" where "visibility is limited" (p. 48). An otherwise featureless plane enshrouded in fog and if not actually infinite, at least larger than all prime material planes put together does indeed seem like a pretty good place to hide something. One could wander such a plane for a very long time before randomly encountering a chest hidden there.
The exception, though, is the Border Ethereal, which is much more circumscribed. The Border Ethereal "overlap[s] the Material Plane and the Inner Planes, so that every location on those planes has a corresponding location on the Ethereal Plane" (DMG p.48). To search for a chest hidden on the Border Ethereal, one need only cover all the likely areas overlapping it on the prime. In particular, if sending a chest back to the Ethereal merely meant translating it to the Border Ethereal location corresponding to its last prime location, then any time you knew the last location of a chest, you could go to that location, cast Etherealness, and look for the chest (possibly prefacing your search with a Dispel Magic aimed at ending the 4th level secret chest spell if the ongoing effect of the spell itself helped hide it).
Having the chest exist on the Border Ethereal might also complicate summoning it, since both magical force and living creatures on the prime create impassible barriers in the Border Ethereal. A titular Jonah who last sent his chest to the Border Ethereal while on land, could not call for it once he was inside the whale, for the chest could not travel to him entirely through the Border Ethereal - it would be stopped at the edge of the whale. A particularly dense forest, where any aperture was smaller than the chest, would also block it. Perhaps most telling, a wizard inside a Tiny Hut would not be able to call for their Secret Chest if the chest was on the Border Ethereal. As the developer of both those spells, one would think the esteemed Mage Leomund would have taken this into account, so that he could in fact summon his own chest while in his hut.
Such a summoning would be possible if the chest was instead hidden on the Deep Ethereal, for the dome of the hut does not extend there. The chest, having received its master's call, would travel through the Deep Ethereal (where "distance is meaningless" - DMG p. 49) and then enter the Border Ethereal already inside the hut, circumventing its barrier effect.
Finally, note also happens when the spell ends - the chest is "irretrievably lost" (and not irrevocably lost, completely lost, or permanently lost). In natural English, something that is irretrievably lost might be found, but it can't be retrieved. It appears that it is the spell itself that retrieves the chest from the Deep Ethereal, and once the spell ends, it becomes 'untethered' and lost in the Deep Ethereal. Were a chest to remain on the Border Ethereal when the spell ended, it should be relatively easy to retrieve.