Drive splash animations by session usage rate

Group splash animations into four moods (idle/normal/active/heavy) and pick
which group plays based on a 5-min sliding rate of session_pct. Thresholds
sit at 0.10/0.20/0.33 %/min so Heavy fires when usage matches or beats the
5-hour session reset pace. Splash auto-rotates within the current group
every 20s; group recomputes on every BLE poll and the splash re-picks
immediately if it changes mid-display. 4-min minimum window prevents
single-sample bumps after boot from falsely landing in Heavy.

firmware/src/usage_rate.h

@@ -0,0 +1,15 @@
+#pragma once
+
+// Tracks short-term rate of change in session_pct (%/min) so the UI can react
+// to *how heavily* Claude is being used right now, not just the current bucket
+// level. Returns one of 4 group indices for the splash to pick animations from.
+
+// Feed in the latest session percentage every time fresh BLE data arrives.
+void usage_rate_sample(float session_pct);
+
+// 0 = idle, 1 = normal, 2 = active, 3 = heavy.
+// Defaults to 0 when the buffer doesn't have enough samples yet.
+int usage_rate_group(void);
+
+// Clear the buffer (e.g. when the 5-hour session window resets).
+void usage_rate_reset(void);