That 'otherwise' seems pretty objectively terrible?
Pay 1 and sacrifice a creature, to pay 1 less. Or, I could just not activate it, for the same net mana cost and not sacrifice a creature?

Given it's SO bad, why not just omit that option?

It's actually amazing: / and sacrifice three creatures for infinite "Whenever a player opens/closes the gate" triggers.

If the gate is open, it's ", Sac: drain 1 life." If the gate is closed, it's either ", Sac: open the gate" or ": Sac." The cost reduction only applies to the next ability you activate

Yeah, if it was "UEOT passage abilities cost less" then that would be abusably good.

But ok, it's now changed to reducing the next cost by . So sure, maybe sometimes you'll want to do that. Not with this as your only gate, so this becomes a "Get lots more passages in your deck" build around. Seems reasonable now.

So... since this is two different effects - one for gate open, one for gate closed - this would be so much cleaner as two separate activated abilities.

­, Sacrifice a creature: Each opponent loses 1 life and you gain 1 life. Activate only if the gate is open.
­, Sacrifice a creature: The next ability of a Passage you activate this turn costs less to activate. Activate only if the gate is closed.

For starters. This also would reduce complexity with instant opening/closing of gates.

Now looking at what you describe I don't see the ": Sac." and I also don't see the value in the hoops you are creating over just:

­, Sacrifice a creature: Open the gate.

Surely the mana reduction might combo with something at some point, but right now your Passages only have one kind of ability benefiting from the three mana, so at this stage of the design, why not write on the card what you actually wrote in the comment?

If this was the only Passage - it would be sensible to make that reduction. The wording makes me assume, however, that the main use of that ability is to make a different passage cheaper to use.

(The "0, sac" was the pointless 'use the same ability twice' possibility. I mean, It's a sac-outlet if you need it, I guess?)

"the main use of that ability is to make a different passage cheaper to use."

This is the only Passage (artifact type) designed so far that even includes a mana cost other than their shared activated ability. Talk about putting the cart before the horse.

The ability changed significantly already - I suggest delaying synergy cards until the cards they are meant to have synergy with exist, otherwise you start designing with the goal to make the ability matter rather than with an ability that is made to enable a group of cards that already can stand on their own.

I further argue that just an cost alternative to for opening the gate has plenty of meaningful synergy with every single already designed Passage for a fraction of the complexity.

Wouldn't the whole point of the gate mechanic be exactly that? Depth coming out of interaction with the gate while saving on shenanigans?

You can make an activated ability on a Passage (or non-Passage!) that "costs less if a player has opened the gate this turn" and get this interaction, too, without loading all the complexity burden into this card.

Most passages won't have other activated abilities. However, there will be other cards that reduce the cost of passages (e.g. Imperial Attendant). I wanted to keep those templated the same where I could