fix(custom-model): isolate Claude config dir and inject real context length

Addresses two live-validation findings on the Run-menu custom-model picker:

1. Both claude.ai and ANTHROPIC_API_KEY set warning. Claude Code still
   coexists an OAuth login with an injected ANTHROPIC_API_KEY in the same
   config directory and warns about it (confirmed cosmetic - the API key
   wins for actual requests, verified via a real session's own API Usage
   Billing line). A custom-model claude session now gets an isolated
   CLAUDE_CONFIG_DIR (registry-declared via a new configDirVar field, empty,
   no files written into it) so there is nothing to conflict with. projects
   is symlinked (junction on Windows) back into the real config dir so the
   response viewer, subagent windows and Read My Mind keep working for that
   session, best-effort.

2. Context-window overflow. Claude Code assumes a large default context
   window for a model id it doesn't recognise and never compacts, so a
   custom endpoint's real, much smaller context (verified live: a 400
   exceeding a 16384-token llama-swap model with a stock ~33.7K-token system
   prompt) silently overflows. Discovery now also learns each model's real
   context length from llama.cpp/llama-swap's GET /props?model=<id> (n_ctx),
   but ONLY for a model llama-swap's own /v1/models response already marks
   status.value === 'loaded' - never an unloaded one, since llama-swap
   treats ?model= as a routing hint and probing an unloaded model risks
   triggering an actual, slow, GPU-swapping load as a side effect of
   read-only discovery. A server with no status field at all gets no
   enrichment rather than a guess; a model not probed this round keeps its
   previously-learned value until it disappears from the list entirely.
   Stored per model (CustomModelHost.modelContextLengths) and applied via a
   new contextLengthVar registry field, set to
   CLAUDE_CODE_MAX_CONTEXT_TOKENS for claude.

Both new fields live on the existing env-kind customModelInjection
capability shape, declared only on claude's registry entry - every other
CLI's injection is unaffected (pinned by test).

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01RqZeHrRS6DYcGcGX2p9EwG

docs/wiki/Custom-Model-Endpoints.md

@@ -27,6 +27,15 @@ hosts — these are machine-level infra, not a per-user setting.
 shows up without another manual click of **Discover**. One endpoint being unreachable on a
 given cycle (powered off, wrong network) never blocks the others from refreshing.
 
+**Context length is picked up automatically where it can be, safely.** Against a
+llama.cpp/llama-swap server, discovery also learns each *currently loaded* model's real
+context window and applies it to the launched session (Claude Code today — see below), so
+the harness stops assuming a large default window for a model name it doesn't recognise and
+overflowing a much smaller real one. It's deliberately never probed for a model that isn't
+already loaded, since asking a llama-swap server about an unloaded model can trigger an
+actual, slow model swap as a side effect — a model just not currently loaded keeps whatever
+context length an earlier cycle already learned for it instead.
+
 ## Running a session against one
 
 With the setting on and at least one endpoint carrying a discovered model, the **Run**
@@ -61,6 +70,18 @@ redirecting those hasn't landed yet, see below. The picker also only appears in
 **Run** dropdown; the phone home screen builds its own run picker separately and does not
 currently offer these entries.
 
+**Claude Code specifically gets two extra fixes applied automatically:**
+
+- Its discovered context length (see above) is passed through as
+  `CLAUDE_CODE_MAX_CONTEXT_TOKENS`, so it doesn't send a full-size prompt against a much
+  smaller real local context and overflow it.
+- Its session runs with an isolated `CLAUDE_CONFIG_DIR`, so the injected API key never sits
+  in the same directory as a stored claude.ai login — that combination is harmless for actual
+  requests (the API key wins) but the CLI still prints a "both claude.ai and
+  ANTHROPIC_API_KEY set" warning about it, which this avoids entirely. The isolated directory
+  keeps a link back to your real session history so the response viewer and similar features
+  still work for that session.
+
 ## Which harnesses actually work
 
 | Harness | Status |