Thank you.
Connecting the signal fixed the misalignment when turning pages.
During scenes with intense movement while viewing pages, synchronization may lag between left and right pages, but we can minimize this by aligning it to one page.
I had overlooked enable_composite_pages.
For the lag, you could connect the signals as deferred (.connect(_any_method, CONNECT_DEFERRED)) so the synchronization is pushed to the next frame, when the engine has some free time, instead of overloading a single frame with both page creation and synchronization.
Alternatively, you could use several awaits to wait a few frames before synchronizing. If it’s a heavy function, you could split it into multiple functions that do a small part each frame, or even use a secondary thread to run the synchronization.
All of these approaches could help reduce the initial micro-lag.