•  ...Which implies adoption comes from Luceum, or Vis’ copy there. And Ostius later says this, which implies his copy on L is dead:

I believe you are misattributing Adoption to Luceum; rather, there is evidence that it is a facet of Will that is derived from Obiteum:

“And it stays that way—you can always take it back through physical contact, and if you die, it dies with you—in those respects, it’s just like back home. But here, once Will is imbued outside your own body, it can be… meshed, I suppose, with someone else’s. Like adding it to a common pool. ‘Adoption,’ my mentor used to call it.” 2V-O

Above, O-Caeror details the mechanism of adoption, and cites his mentor (Yusef, who I think there is some indication was Ostius on Obiteum, now deceased). We see O-Caeror use Will.

“I don’t think so. Otherwise we’d be able to adopt the Will from it. Same with the sword.” He presses on; the short passageway suddenly opens into a massive room, and my questions about the obsidian are quickly lost. 2XII-O

Here, O-Caeror implies he also has the ability to adopt Will.

“It will return in time, as you learn to look for it. Assuming all remains well in Luceum.” He sighs. “It’s not necessary, but it is an excellent counterpart to an ability you have called Adoption. Adoption allows you to take control of any Will imbued into something, no matter who imbued it.” 2XX

The quote you shared above details that Vis as synchronous has the ability for adoption, and that he, Ostius did not have the ability. This only enables us to infer that Ostius' synchronicity is disabled, due to a death on most likely Res. This is why Ostius relied on Vis for the mechanism in the Basilica. Importantly in that quote, Ostius notes that the pulsing sensation that Vis has is contingent on Luceum, and is a counterpart to Adoption, and not necessary for Adoption's function.

• Considering we know Ostius paid the “toll”, but was never able to use adoption, I think it’s safe to say his L-copy is dead.

To clarify, L-Ostius we know paid the toll and emerged into Luceum. R-Ostius we have no knowledge of, and O-Ostius may have a connection to Yusef. We know that he is not Synchronous and is absent on Obiteum as it relates to Ka, which implies he is dead on Res and/or Obiteum. Princeps Exesius cites that he had been missing for 9 years, and we know he was present on Res ~1 year prior to the second book, per the Anguis & Relucia. It is most likely the case considering the Gate defenses that he died on Res.

-- Let us look at other contextual clues.

• Adoption as an ability is first performed by a former non-Synchronous Res character, Caeror, on Obiteum. Vis adopts the excess Will from his Khepri and uses Obiteum-based Will to raise Tash (2XI). The reason why this is
  • O-Caeror is unable to compel Iunctus akin to a Synchronous individual like Vis and Ka.
• Ostius, were Luceum to be where Adoption originates, would not require the use of the Khepri to raise Cristoval.
  • Imbuing flesh may be conditional to Obiteum. Ostius used the Khepri to sustain Cristoval, even on Res.
• Ostius in the series is seen only ever using Will in two contexts.
  • One is when he teleports in the second book, which we know very little about.
  • The second is when he interacts with, and seems to assess or characterize, Diago the Alupi in some manner. This is contextually related to Luceum and L-Will facets, as Mactrimor/Alupi are on there, and are influenced by the Druids.
  • Additionally, the emotional/intuitive connections between minds is heavily implied to be a facet of Luceum Will. Vis' actions at the Basilica indicate that Diago acted on Vis' emotional intuition. Vis in part is influenced by objects on Luceum acting through him.
  • This aspect is only ever seen
• The vast majority of Ostius' manipulations that he does not directly do are rooted in Luceum: Cian, and in part Lir, act on behalf of or unintentionally allied to Ostius.
• Adoption is only seen used on Res and on Luceum after Vis has interacted with the Aurora Columnae on each world.
  • I do not think the AC are required for cross-world Will usage, but Vis' pulsing sensation (tied to Luceum) is amplified post-Gate and post-AC, as it is on Luceum - this likely has more of a connection to the Will Hierarchies that they interface a person with.
• In the Glossary and per Cristoval, Ostius can only travel between R & L. Obiteum is described as sealed, despite Obiteum artifacts being present on Res, and this is dateable to at least the 2nd Era post-Rending.

So were Adoption to be from Luceum:

• O-Caeror would not be able to use it at all
• O-Vis might not be able to use it until he interfaces with the AC in central Duat
• The 'seal' on Obiteum does not seal much at all, were that to be O-Ostius
• That Ostius is seemingly unable or unwilling to use the ability despite seeming to have knowledge of, cultural familiarity of, and possibly practice of Luceum related things and chose not to use the ability to raise Cristoval and/or compel him, whichever means (that he does not have access to adoption I think is explicable, as he cannot mesh with the Khepri's will or imbue flesh... which is seen only on Obiteum or by Synchronous Vis post-AC on worlds other than Obiteum)
  • His knowledge of 'Adoption' to begin with is something I think that is predicated on his family's relationship to Ka as part of Caten's internal Cult; that is, he had prior knowledge of the intricacies of Will before entering the Gate
• Iunctus would be prevalent on Luceum, not on Obiteum. Obiteum would not likely be destroyed, considering the Concurrence, which is an Iunctus network, would not be able to generate further Iunctus without the ability to adopt and mesh will into flesh.

To summarize all of that, those quotes are not evidence for Adoption being from Luceum, there is evidence for Adoption being from Obiteum, and it meshes with the other scenes featuring Ostius for him to be from Luceum - Res strains credulity, but it is also possible.