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[RandomPeasant]

You are talking about two different events that are not the same. You don't have a caster level. There is nothing there for the staff to use. What you do is emulate a caster level to get access ("activate") the abilities of the staff (if mandated).

The timing distinction you are carving out here does not exist. The activation is one step. The description of staves says that the CL used during that step replaces that of the staff if it is higher. There is simply no opportunity for a CL to apply to "can you use the staff" but not "what does the staff do".

If the staff description gave a +2 DC for a specific ability score, that is, it has a gatekept feature, then you get the +2 DC. Otherwise you get nothing except your own relevant ability score.

Again, this is just saying that you can benefit from enumerated ways to post DC from ability scores, but not general ones, without any basis for that distinction.

Let me redirect you to your mentioning of STR. If a weapon is gatekept for a feature, say +2 electricity damage at 20 STR, are attacks by the character using that weapon now made at 20 STR? If not, why not? It's consistent with your interpretation.

If a magic sword said "you can add your STR bonus to damage rolls with this weapon", you could absolutely UMD up a big bonus by emulating a high STR. But magic swords don't say that, because the ability to add your STR bonus to weapon damage is a normal rule. The ability to use your person attributes for item DCs, on the other hand, is very much a special property of staves, and therefore eligible for emulation.

I mean, you have yet to show where the description says the item requires you to actually turn undead. Once you do that I'll show you how to turn without expending resources.

"You have yet to show where the description that specifically mentions turning undead mentions turning undead."

It is, if that was unclear, the place where it explicitly mentions turning undead.

UMD is used TO activate an item. If an ability score or caster level isn't required to use the item, why would the skill allow you to emulate having it so?

And now we're back to "you can't UMD a staff of power because it can be used as a weapon without a roll". The ability to use one functionality of UMD to engage with an item does not preclude using others. The idea that it does instantly creates wide swathes of dysfunction throughout the game.

They do have a minimum caster level for a reason.

No one is claiming that you can't activate a staff without emulating a caster level. I don't understand why you keep pointing to stuff that is completely explicable like it is some giant hole in the rules, particularly when you also bash open giant holes in the rules like "it is impossible to UMD a staff of power".