separate
We use the verb change because if the rule didn't say otherwise the additional damage wouldn't be necrotic.
We want to point out that the rule specifically changes the additional damage into something useless against the foes the subclass purportedly fights against.
We want to highlight the fact that the additional damage would be strictly better if the rule didn't specifically call out the absolute worst damage type (after poison) for the character concept as described.
There's nothing wrong with restrictions to abilities. But don't give out something that is decidedly useless against the intended targets.
I think that that is being a little incorrect there. Without the ability, there is no additional damage. It isn't changing existing additional damage, it is changing an existing effect into the same effect with added necrotic damage. Its not changing a 2d8 Bludgeoning mace strike into a possibly less damaging strike, its changing a d8 Bludgeoning mace strike into a d8 bludgeoning + d8 Necrotic strike.
I'm aware that you think that the additional damage should be of another type. But what you were saying was potentially giving the false impression that the ability was making an existing capability worse, rather than making it better, but not in the most optimised fashion.
But this is also an ability (as written) that has spurred a lot of dissent in the UA domain thread, here and elsewhere, due to the nature of how it depends too heavily on GM fiat. You use your ability. Your GM doesn't know. You have wasted your ability. That's one of the reasons why I support a revision to this ability such that it can be applied more readily, broadly, and reflect a wider range of the archetype's responsibilities that you have mentioned before. Doom awaits as the grave cleric knows your hit points, hit dice, and or other weaknesses.
Why does your DM not know whether there are undead within 1 mile? Its not like they are a common occurrence in the world normally, and a mile is not a huge area unless you're in building-scale operation - at which point the DM should have a pretty good idea whether there are undead in the city or not.
Its only every short rest, so it can't be used repeatedly, and the default is going to be none unless you're close enough to an area plot-relevant enough for the DM to know whether there are undead there or not.
I disagree with your initial assertion. The grave cleric exercises little control over their channel divinity ability as they are instead overly reliant upon whatever damage source provides the next hit. They have no control over what or when that might be. That is way too "swingy" and chaotic. There is little to no agency in that. A knowledge cleric can read thoughts. A life cleric has controlled healing. A light cleric summons a blinding light. A nature cleric can charm plants and animals. A tempest cleric can maximize elemental dice damage. A trickery cleric can cast an illusionary duplicate. A war cleric can imbue +10 to an attack. A death cleric can deal extra necrotic damage when they hit. The channel divinity options of the published cleric domains all demonstrate a greater degree of agency than what the grave cleric gets when they make the choice to expend their alternative channel divinity option.
So your objection is that it is too much of a teamwork and not a personal DPS capability? The cleric is losing agency because another party member could be the one to deliver the strike that the target would be vulnerable to?
If the ability specified that it was only the next spell or attack
from the Cleric that the target was vulnerable to and that would use up the ability, would that be better? (Possibly also make activating it a bonus action ? Or would that be a bit too powerful?)
For the record, the old specialty priests for Kelemvor back in 2e allowed for a second attempt to turn undead. That sounds like giving advantage on turn undead attempts would be appropriate for Grave clerics. That could be given as part of their 2nd level feature. It enhances the Channel Divinity feature that they also get at 2nd level. Then maybe a Grave cleric's Channel Divinity, which we could also call Eyes of the Grave, could then pertain to locating undead as well as determining the hit points, vulnerabilities/weaknesses, resistances/immunities, and such of a given foe.
Advantage to turning undead is a good idea: it doesn't allow a cleric to do anything too powerful that they couldn't do already, it just makes them better at it.
I wouldn't mess with the second ability though. Path to the Grave is an interesting effect that will work on most creature types, and represents the idea that death can come for anything. Turning it into just another anti-undead ability would not only overly focus the subclass onto a single aspect of its theme, it doesn't give the cleric an ability that it can use in more general circumstances. As you have demonstrated earlier, most domain-specific channel divinity abilities are giving an option for the ability that can be used more generally.