There are 3 tomes that Parallel Daisy back has access to that Standard Daisy back does not: Grimm's Fairy Tales, Scroll of Prophecy (3) (Mystic), and Book of Shadows (3). Of those three, Book of Shadows is by far the most interesting. Parallel Daisy back has access to the Archaic Glyphs spells, which use charges, rather than secrets (and so can't be recharged with Astounding Revelation). Book of Shadows could conceivably guarantee a use of Guiding Stones every turn, which is pretty strong. Where this starts to get really exciting, in my opinion, is with the upcoming Astronomical Atlas, which allows you to commit the top card of your deck to a skill test and add it to your hand if you succeed. Add in Practice Makes Perfect and you're well on your way to big commit Daisy deck that can just scoop up mountains of clues very consistently on higher player counts.

Ironically, most interesting for Carolyn Fern, as a 0-cost way to permanently and efficiently deal with smaller enemies spawning atop you (potentially even combining it with Beat Cop or other testless damage to handle 3-health enemies), as she typically doesn't have many enemy management options (especially not so cheap and guaranteed). Theoretically very useful if you want the deck to have more independence from other investigators, or if there's no enemy fighter on the team (e.g. playing solo).

Plus, you know, it's amusing. Who needs orderlies now?

(And definitely a useful card if going for a gimmick build with Meat Cleaver.)

When waylay came out with a pallid mask, it could do some good work.
Adventures since (and Carcosa's return) have given us more difficult enemies, five or six or seven hit point foes, who aren’t elite. Yet, despite being 0xp, this card is best as a skill commit until mid adventure. Lola, Wendy, Preston… all three can use adaptable to swap it in. And it’s expensive, but a rogue splash or on your own can handle that. Your mileage may vary.

Your friendly neighborhood Buttermancer here to strongly recommend against running this card in The Circle Undone, given the huge amount of deck milling mechanics in that campaign. You'll whiff right past it at a million miles an hour. Probably twice after the encounter deck shuffles. You might draw it if you have encounter deck peeking shenanigans, but even then not reliably enough to make playing it worth the action.

In campaigns where the encounter deck is not flying off the table out the window, it looks pretty intriguing, probably strongest at 2 players given its unique requirements and effect. To elaborate, for one player, ten cards in the encounter deck is basically guaranteed, but play Stargazing halfway through a scenario and shuffle it into the bottom and you probably won't see it before the scenario is resolved. It does cancel 100% of spooky card bad stuff when it lands.

Two players probably have plenty of cards in the encounter deck and will draw the card within 5 turns, reasonable if it's at all early. It will cancel 50% spooky card draw for the team on the turn it lands. After that, it gets worse. It will be drawn very soon but only cancel a third of the encounter deck, and it will be drawn almost immediately but cancel the effect on 1/4th the team. It's actually a pretty good play on Farsighted (Mandy and Daisy can fit these, and Daisy has big hands potential synergy in Forbidden Tome).

"Other card abilities or game effects do not resolve with the altered game state in mind; only the indicated ability/action. - FAQ, v.1.7, March 2020"

This information is outdated. The FAQ v 1.8, October 2020 states instead that

"Other card abilities or game effects resolved during this duration are also resolved with the altered game state in mind."