How does the shadows mechanic (and specifically something like alchemist guild hall) work with the Jaime that stands at the beginning of each phase now that shadows is after the beginning of phase but still part of the same framework window? I assumed it would kneel Jaime now, but it was pointed out that shadows mechanics have to resolve (including all responses) before moving over so I'm not entirely certain. . .

Bringing a card out of Shadows is considered its own complete action. The complete action includes all passives and Responses to that card coming out of Shadows. The rules also say that all cards come out of Shadows before other passives or Responses for the phase begining take place. Combine those two rules and you get that the Guildhall will kneel a character before Jaime's passive kicks in and stands him at the beginning of the phase.

(Yes, I know that the flow charts have "bring cards out of shadows" as a framework event now, which would imply a somewhat different timing. But the rules text is very clear that bringing cards out of Shadows should be treated as a separate action. Follow the actual rules text, not the representation of the rules in the flow chart. For example, if you take the flow chart as the "last word" in timing, there is no Epic phase ever, right?)