If my unit dies and I use Zhonya's Hourglass or Guardian Angel to save it, does it count as choosing the unit?

No, using Zhonya's Hourglass or Guardian Angel to save a unit does not count as "choosing" or "targeting" that unit.

According to Rule 352.10.c, a game object mentioned in a replacement effect is not a target if it is included only as part of the replacement effect's condition. Because these cards function as replacement effects (identified by the word "instead" per Rule 366.1), they do not target or require you to "choose" the unit in the way a spell or ability would.

Here is the breakdown of why:

• Replacement Effects: Both Zhonya's Hourglass and Guardian Angel are replacement effects that intercede when a unit would die. They automatically apply to the event of the unit dying.
• No Targeting: Because they do not target, they bypass targeting restrictions and do not trigger any abilities that care about a unit being "chosen" or "targeted."
• Simultaneous Deaths: If multiple units would die simultaneously (such as in combat), you (as the controller of the gear) do choose which death event to replace, but this is a choice of which event to modify, not a choice of a target for an ability.

Important Nuance: If you have both Zhonya's Hourglass and Guardian Angel on the same unit and it dies, you choose which replacement effect to apply (as per FAQ #834). Once you choose one, the other no longer has a valid trigger condition because the unit never actually died.