feat: Add presence heartbeat for Matrix online status

- matrix-gateway: POST /internal/matrix/presence/online endpoint
- usePresenceHeartbeat hook with activity tracking
- Auto away after 5 min inactivity
- Offline on page close/visibility change
- Integrated in MatrixChatRoom component

node_modules/fraction.js/examples/angles.js

@@ -0,0 +1,26 @@
+/*
+Fraction.js v5.0.0 10/1/2024
+https://raw.org/article/rational-numbers-in-javascript/
+
+Copyright (c) 2024, Robert Eisele (https://raw.org/)
+Licensed under the MIT license.
+*/
+
+// This example generates a list of angles with human readable radians
+
+var Fraction = require('fraction.js');
+
+var tab = [];
+for (var d = 1; d <= 360; d++) {
+
+   var pi = Fraction(2, 360).mul(d);
+   var tau = Fraction(1, 360).mul(d);
+
+   if (pi.d <= 6n && pi.d != 5n)
+      tab.push([
+         d,
+         pi.toFraction() + "pi",
+         tau.toFraction() + "tau"]);
+}
+
+console.table(tab);