Vision within the Ethereal Plane is obscured by fog, which the Robe of Eyes cannot pierce
In the passage you quoted, the limited visibility in the Deep Ethereal is specifically described as being caused by "swirling mist and fog". Hence, we can infer that visibility is limited because anything beyond 30 feet is heavily obscured by this fog, as described in the rules for Vision:
A heavily obscured area--such as darkness, opaque fog, or dense foliage--blocks vision entirely. A creature effectively suffers from the blinded condition when trying to see something in that area.
As for the Border Ethereal, the part you quoted doesn't give a reason for visibility being limited to 60 feet, but earlier in the same paragraph, we have:
The Ethereal Plane is a misty, fog-bound dimension.
From this, we can reasonably conclude that the 60-foot limit on sight in the Border Ethereal is likely also because anything beyond that distance is heavily obscured by fog.
So, can the Robe of Eyes pierce this fog? Looking in the description, there is nothing about seeing through heavily obscured areas (except those caused by darkness), which means the Robe cannot pierce the obscuring mist and fog in the Ethereal Plane, and is unable to extend your sight range while in the Ethereal Plane. Note that this is likewise true of effects that grant truesight. In general, a non-vision-based sense, such as blindsight or tremorsense, is required to effectively perceive something that is heavily obscured.
So why can the Robe see 120 feet into the Ethereal when on the Material Plane?
Having settled things according to the rules, we could leave things there, but it's reasonable to ask how it's possible for that a vantage point in the Material Plane could improve Robe of Eyes' visibility into the Ethereal Plane, relative to being in the Ethereal Plane itself. The simple answer is that the fog of the Border Ethereal does not obscure vision on the Material Plane, even for a creature that can see into the Ethereal Plane. If it did, then any effect that granted vision into Ethereal Plane would also limit your sight range to 60 feet, which would in turn limit all truesight on the Material Plane to 60 feet. This is very likely not the intent, given that a number of game effects grant truesight with a longer range than 60 feet.
