Bug: when the StreamDeck was on a non-main page (e.g. dashboard) and the
web UI was opened in a private browser tab, the frontend defaulted to the
first page in config while display outputs from the other page were still
applied to keys sharing the same index.
Fix 1 (backend): send the current active page via SSE immediately on new
client connection so the frontend knows the correct page from the start.
Fix 2 (frontend): only apply display output text/background to keys that
have a display config, preventing cross-page leakage.
