README down to what a user needs; the rest into docs/

The README had grown to 1,010 lines of user docs and design notes in one file,
and had gone stale: it still showed the old numbered menu, set up only three
providers, and listed preflight checks and a file layout that predate the last
three releases. It now carries install, first run, the full command
reference, the providers at a glance, troubleshooting and a docs index.

docs/:
- providers.md    presets, defaults, the model cache, context windows, each
                  provider (OpenRouter's cost guard and guardrail check are
                  written up for the first time), adding a provider
- live-sessions.md  what a switch does to running sessions, and repair
- design.md       why settings.json, why keys stay out of it (and the vault
                  per platform), the preflight checks as they are now
- bar-widget.md   the widget as it is now: providers from health.json, every
                  server provider's settings, the restart after an upgrade
- architecture.md the pieces, every file on disk and who writes it, the
                  contracts between them, where to change what
- development.md  running the tests, the conventions the code follows,
                  working on the widget, releasing
CONTRIBUTING.md points at it.

Also:
- The per-project session listing used awk, which the CLI avoids because it
  is missing from minimal images; it uses the script's own TSV helpers now,
  and tests/static.sh fails on any awk in the CLI.
- tests/static.sh checks every relative Markdown link and #anchor.
- A unit test pins the managed env keys between cm-json.py and
  claude-mode.ps1, which only a comment kept in step before.
- test_sessions covers the per-project listing, which nothing ran.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

tests/python/test_cm_json.py

@@ -89,6 +89,19 @@ class Providers(unittest.TestCase):
             with self.assertRaises(SystemExit):
                 call(cm.cmd_provider_resolve, [word])
 
+    def test_managed_keys_match_the_windows_build(self):
+        # A key one build clears and the other does not survives a switch on
+        # that platform - "must stay in lockstep" was only a comment until this.
+        import re
+        with open(os.path.join(REPO, "claude-mode.ps1"), encoding="utf-8") as fh:
+            ps = fh.read()
+        # Up to the line that is only ")", not the first ")": the array's own
+        # comments contain parentheses.
+        block = re.search(r"\$script:BaseManagedEnvKeys\s*=\s*@\((.*?)^\)", ps, re.S | re.M)
+        self.assertIsNotNone(block, "BaseManagedEnvKeys not found in claude-mode.ps1")
+        body = "\n".join(l for l in block.group(1).splitlines() if not l.strip().startswith("#"))
+        self.assertEqual(sorted(re.findall(r"'([A-Z0-9_]+)'", body)), sorted(cm.BASE_MANAGED))
+
     def test_static_catalogue(self):
         self.assertEqual(call(cm.cmd_provider_static, ["zai"]).splitlines()[0].split("\t")[0], "glm-5.3")