Connect to server over websocket for live cloud sync

Desktop app now holds a persistent websocket to the server and syncs
on push notifications instead of a fixed timer, falling back to the
old polling interval only when the socket is down. Cloud folder/file
listings are cached locally so the browser stays usable offline.

Claude-Session: https://claude.ai/code/session_01PoLmSR1pFVyHf8i5b1rNWk

src-tauri/Cargo.lock

@@ -947,6 +947,12 @@ dependencies = [
  "syn 2.0.119",
 ]
 
+[[package]]
+name = "data-encoding"
+version = "2.11.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "a4ae5f15dda3c708c0ade84bfee31ccab44a3da4f88015ed22f63732abe300c8"
+
 [[package]]
 name = "data-url"
 version = "0.3.2"
@@ -3889,6 +3895,8 @@ version = "0.8.7"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "22f6172bdec972074665ed81ed53b71da00bfc44b65a753cfde883ec4c702a1a"
 dependencies = [
+ "libc",
+ "rand_chacha",
  "rand_core",
 ]
 
@@ -3907,6 +3915,9 @@ name = "rand_core"
 version = "0.6.4"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "ec0be4795e2f6a28069bec0b5ff3e2ac9bafc99e6a9a7dc3547996c5c816922c"
+dependencies = [
+ "getrandom 0.2.17",
+]
 
 [[package]]
 name = "raw-window-handle"
@@ -4558,6 +4569,17 @@ dependencies = [
  "stable_deref_trait",
 ]
 
+[[package]]
+name = "sha1"
+version = "0.10.7"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "a978451301f4db1d02937a4ab3ccce137717b81826e79b7d49ffe3244a13c3b8"
+dependencies = [
+ "cfg-if",
+ "cpufeatures",
+ "digest",
+]
+
 [[package]]
 name = "sha2"
 version = "0.10.9"
@@ -5705,6 +5727,25 @@ dependencies = [
  "core_maths",
 ]
 
+[[package]]
+name = "tungstenite"
+version = "0.24.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "18e5b8366ee7a95b16d32197d0b2604b43a0be89dc5fac9f8e96ccafbaedda8a"
+dependencies = [
+ "byteorder",
+ "bytes",
+ "data-encoding",
+ "http",
+ "httparse",
+ "log",
+ "native-tls",
+ "rand",
+ "sha1",
+ "thiserror 1.0.69",
+ "utf-8",
+]
+
 [[package]]
 name = "two-face"
 version = "0.4.5"
@@ -5778,6 +5819,7 @@ dependencies = [
  "tauri-plugin-clipboard-manager",
  "tauri-plugin-dialog",
  "tauri-plugin-opener",
+ "tungstenite",
  "typst",
  "typst-assets",
  "typst-html",
@@ -6345,6 +6387,12 @@ dependencies = [
  "xmlwriter",
 ]
 
+[[package]]
+name = "utf-8"
+version = "0.7.6"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "09cc8ee72d2a9becf2f2febe0205bbed8fc6615b7cb429ad062dc7b7ddd036a9"
+
 [[package]]
 name = "utf16_iter"
 version = "1.0.5"