Watch supports before Part 1 ends: replaying old chapters may leave the Promised One campaign lockedMajor spoilers
Watch available conversations during Part 1. Replaying them in old chapters and unlocking the next conversation in the current Promised One campaign can show different menu states.
Original video: [Fortune's Weave] Watch every available support conversation before Part 1 ends!! Contains five-years-later portrait spoilers; Bilibili creator Kakaluoka Q; https://www.bilibili.com/video/BV1DfHD6nEV9/
Watch available Part 1 supports promptly
I assumed that because the hall lets you switch chapters anytime, missed Part 1 supports could simply be watched later. After clearing the game, I discovered that watching them in an old chapter does not necessarily unlock the next scene in the current Promised One campaign.
Some supports say they cannot be viewed in the current part, with scenes divided across parts. If you skip them while rushing ahead and return later, the next scene may still be locked.
Different menus in Parts 1 and 3
I returned to 
Theodora’s Part 1 route and opened one of 
Mu’s support chains. C had been watched, and B was available. Switching back to Part 3 left the corresponding slot locked.
The Altar of Causality’s review also contained the watched C scene. Having the scene in the review and being able to play the next scene in the current campaign were therefore visibly different states.
The idea of replaying chapters after catching up
My theory is that Part 3 reads the record from clearing Part 1. Going back to watch scenes now does not update that clear state, so Part 3 does not change.
Next, I plan to return to Part 1, finish conversations restricted by part, and clear Chapter 12 again. Missing them across all four routes would make replaying troublesome. If you are still in Part 1, watch available supports as they appear instead of leaving everything until the end.