A replay's Capture always wrote to the local library, so a signed-in
user's captured strategy landed on this device while the rest of their
work was in the cloud. Signed in, Capture now makes the strategy in the
cloud (the open cloud folder, else the top level) and adds each captured
page there; signed out it stays local as before.

Each cloud capture is one page and its items sent together; one that
doesn't land is taken back and the user is told. Offline it refuses with
a message rather than queueing: a cloud strategy can't be made offline,
and the replay is still there to capture from. Items get fresh ids (the
server keys them globally) with one root per player across pages, so
page transitions still move players between captured moments. Open
lands on the last captured page for cloud strategies too.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>