Zhonya's Hourglass dies as a unit gear, will Zhonya's Hourglass see itself and recall

No — a Zhonya's Hourglass that's been turned into a unit gear (e.g. via Lady of Clockwork) does not save itself when it dies.

It does "see" its own death: while it's a unit gear it's a friendly unit, so its replacement effect applies to its own death — Rule 370.2's example literally has a gear-unit Hourglass's effect applying to its own death. But the applied effect is "kill this instead," so the Hourglass gets killed, which is the death that was already happening. The "heal that unit, exhaust it, and recall it" then has nothing to reach, because the Hourglass is in the trash rather than on the board, and a replacement effect can't be applied twice to the same death (Rule 370.2).

The self-save only works with two copies: the second Hourglass's effect replaces the kill of the first (Rule 370.2), so one survives and the one whose effect is applied last is the one that dies — you pick that order. None of this uses the chain; replacement effects apply on their own.