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>

linux/claude-mode

@@ -2831,7 +2831,7 @@ print('  %sprovider\'s ids by design and resume fine under it%s' % (D,X))
         # the scan, so it asks the scan which ones are hidden. It still shows
         # them - listing everything here is its job - but says why the bar
         # is not counting them.
-        local f v hidden reason
+        local f v hidden reason row
         hidden="$("$PY" "$JSON" scan-sessions "$CM_SETTINGS_DIR/projects" "$max_age" "$CM_IGNORED" 2>/dev/null \
             | "$PY" -c "
 import json,sys
@@ -2842,7 +2842,10 @@ for i in d.get('ignored') or []:
 " 2>/dev/null)"
         for f in $(ls -1t "$dir"/*.jsonl 2>/dev/null); do
             v="$("$PY" "$JSON" repair-session "$f" 2>/dev/null)" || continue
-            reason="$(printf '%s\n' "$hidden" | awk -F'\t' -v s="$(basename "$f" .jsonl)" '$1 == s { print $2; exit }')"
+            reason=''
+            if row="$(printf '%s\n' "$hidden" | tsv_find "$(basename "$f" .jsonl)")"; then
+                reason="$(tsv_field "$row" 2)"
+            fi
             printf '%s' "$v" | "$PY" -c "
 import json,sys,os
 d=json.load(sys.stdin)