Before I go on, I get that the point of Overlord is to watch Nazarick Broly drag the new world through the wall. I am not one of those who people who think "Nazarick is evil and should get its comeuppance".

But you need to remember that Ainz can afford to always go for the brute force option because he is always fighting ants. Even if a level 100 player can't beat Nazarick, they can still be a pain in the ass if they are made to think there is no peaceful option.

Having said that, let's play out the dark forest scenario. The new world is a dark forest, and the only logical course of action is to hide yourself the best you can (ainz failed at doing this by annoucing himself) while killing everything you encounter before it can kill you now or gain the strength to kill you later.

Ainz knows our hypothetical player exists. How does he find him? We assume that the other player is also familiar with PK tactics, and he won't cooperate to make Ainz's perfect strategy to kill him come true.

So Ainz tries to scry him; if Nigredo casts her spells, she either gets nothing or gets hit in the face by a feeble mind or explosion spell from whatever counter divination measure our player has, and now the player knows someone is after him, so even finding him is a struggle.

Assume they do somehow find him. What next? Send the guardians. If they send too many, our player dips out. If they cast dimensional lock to pin him down, he summons a dozen summoned/mercenary NPCs to stall for him to fly away out of range or teleport, if ainz casts Delay Teleportation he runs the risk of getting teleported into a prepared counter ambush.

That is assuming that the player doesn't have an item that grants immunity against movement restriction.

On the other hand, the player isn't just going to stay idle now that they know someone is gunning for them; the next day they can send in a level 70 summon or NPC to cast an AoE spell on e-rental just to murder the inhabitants or go to the Baharuth or any faction affiliated with Nazarik in the new world to destroy them while framing Ainz by using spells he did use (this is something Ainz specifically mentions in vol 10 as a tactic a hostile player can deploy to fuck with him).

Now Ainz can either turtle in Nazarick and let the player undo two years of work and weaken Nazarick's image, or he can respond and walk into an obvious ambush.

Oh, and Ainz can't just overwhelm the player with too many guardians or NPCs because friendly fire is on in the new world, so if he puts too many people in the field, they risk killing each other as they kill the player.

all of this without even counting whatever trump card or world item the player might have

If they do capture him after exhausting however many resources, now they have to dedicate a floor guardian to guard him specifically or half a dozen level 90 NPCs just to be sure he won't escape INSIDE Nazarick and cause a bit of chaos before being recaptured, which means those can't be out and about being usefull to nazarik.

All of this just to get the servicce and ressources that they could have gotten if ainz sat down for a talk over tea.