Only Arcane Hand may have some effects on creatures in the Bordered Ethereal: it's a DM call.
The reported quote says (emphasis mine)
A traveler on the Ethereal Plane is invisible and utterly silent to someone on the overlapped plane, and solid objects on the overlapped plane don’t hamper the movement of a creature in the Border Ethereal. The exceptions are certain magical effects (including anything made of magical force) and living beings.
Hence, these rules are specifically related to movement: Mordenkainen's Sword has nothing to to do with movement, whilst the Arcane Hand can affect the movement of a creature:
Forceful Hand. The hand attempts to push a creature [...]
Grasping Hand. The hand attempts to grapple a Huge or smaller creature [...]
Interposing Hand. The hand interposes itself between you and a creature you choose [...] The target can't move through the hand's space if its Strength score is less than or equal to the hand's Strength score. [...]
But the description of the spell does not specify that these options can be used also on creatures in the Bordered Ethereal. For comparison, consider the Wall of Force spell (emphasis mine):
Nothing can physically pass through the wall. It is immune to all damage and can't be dispelled by dispel magic. A disintegrate spell destroys the wall instantly, however. The wall also extends into the Ethereal Plane, blocking ethereal travel through the wall.
Since there are some feature of the Arcane Hand that are related to movement and the rules in the DMG seems to be related only to movement, a DM may rule that such spell affects creatures in the Bordered Ethereal.
A more lose reading of the rules in the DMG about the Bordered Ethereal leads to consider both spell affecting creatures in the Ethereal plane, since both the sword and the hand are clearly made of magical force.