The False Hoturi

Legend of the Five Rings card from Promotional–Imperial

Card Type: Personality
Force: 3
Chi: 5
Honor Requirement: -
Gold Cost: 9
Personal Honor: 0
Clan: Scorpion
Keywords: Unique, Deceiver, Samurai, Scorpion Clan
Card Text: This card is considered The Egg of P'an Ku for deck construction and checking the Unique restriction.
Will not join a Crane Clan player.
Repeatable Limited, w: All Crane Clan players lose 2 Honor.
Legality: Clan Wars (Imperial)
Deck: Dynasty
Notes: Art forms a diptych with The Farther You Fall.

Printings

Rarity: Promo
Flavor Text: "He is not you, my dearest Hoturi, he is better than you. But the others will believe he is you, and while I hold you here, he will be the doom of your Clan."
Artist: Matt Wilson
Publisher: Five Rings Publishing Group

Q: part in bold covers Unique, Loyal and "will only join / will not join".
covers Singular.
so, yes, it can copy anything.
well, anything unless The False Hoturi is in play because he counts as the Egg for uniqueness, unlike Tamago who counts as the Egg for deck construction.
A: The trick to Egg of P'an Ku is that it enters play first (under your control) and then it copies the targeted card (gaining Singular, Loyal, or what have you).
Those Rules don't prohibit cards you already control gaining those traits, just you gaining control of cards which have the trait already.
As for Daizu, having used his trait is not a change to Daizu's Card. It is simply an in-game event that everyone remembers. The Egg hasn't used the trait yet, even if it copies a Daizu who has done so. It is still a distinct card from that copy of Daizu. Martin Lund, "A Couple More Egg Questions", 15 Feb 2005
Q: I remember getting the false Hoturi and I momentarily became obsessed by the narrative around it
A: I also have a shirt of unreleased Kachiko art by Paul. AEG rejected it because he drew her with her hair down. Brook Cunningham, "Oracle of the Void #rules", 21 Apr 2023