feat(llm): adaptive num_ctx tiers + fix KV cache priming num_ctx mismatch

Adds pick_num_ctx() which selects the smallest context window tier
(8192, 16384, 32768) that fits the current messages with 25% headroom,
capped at OLLAMA_NUM_CTX. Threads num_ctx through generation_task.py so
every chat request uses the computed tier rather than a fixed 16384.

Fixes a critical cache miss bug: KV cache priming in app.py and
settings.py was sending requests without num_ctx, so Ollama sized the
cache at its model default (different from the 16384 real requests used),
forcing a full model reload on the first real user message. Both priming
sites now call pick_num_ctx() and pass the matching value.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

src/fabledassistant/services/llm.py

@@ -19,6 +19,28 @@ from fabledassistant.services.settings import get_setting
 
 logger = logging.getLogger(__name__)
 
+# Context window tiers. The smallest tier that fits the current input is used
+# so Ollama allocates a smaller KV cache, reducing prefill time and VRAM usage.
+# Requests using the same tier hit Ollama's prefix cache; a tier upgrade causes
+# a one-time model reload but then the larger cache stays warm.
+_CTX_TIERS = (8192, 16384, 32768)
+
+
+def pick_num_ctx(messages: list[dict]) -> int:
+    """Return the smallest context tier that fits *messages* with 25% headroom.
+
+    Stays at or below Config.OLLAMA_NUM_CTX (the configured ceiling).
+    """
+    total_chars = sum(len(m.get("content") or "") for m in messages)
+    estimated_tokens = int(total_chars / 3.5)
+    needed = int(estimated_tokens * 1.25) + 256  # 25% headroom + output buffer
+    cap = Config.OLLAMA_NUM_CTX
+    for tier in _CTX_TIERS:
+        if tier >= needed and tier <= cap:
+            return tier
+    return cap
+
+
 STOP_WORDS = frozenset({
     "a", "an", "the", "is", "it", "to", "in", "for", "of", "and", "or",
     "on", "at", "by", "with", "from", "as", "be", "was", "were", "been",
@@ -112,6 +134,7 @@ async def stream_chat(
     model: str,
     options: dict | None = None,
     think: bool = False,
+    num_ctx: int | None = None,
 ) -> AsyncGenerator[str, None]:
     """Stream chat completion from Ollama, yielding content chunks.
 
@@ -119,7 +142,7 @@ async def stream_chat(
     Thinking tokens are silently discarded anyway, but disabling avoids the
     multi-minute delay before the first content token arrives.
     """
-    merged_options = {"num_ctx": Config.OLLAMA_NUM_CTX}
+    merged_options = {"num_ctx": num_ctx or Config.OLLAMA_NUM_CTX}
     if options:
         merged_options.update(options)
     payload: dict = {"model": model, "messages": messages, "stream": True, "options": merged_options, "think": think, "keep_alive": "2h"}
@@ -159,6 +182,7 @@ async def stream_chat_with_tools(
     model: str,
     tools: list[dict] | None = None,
     think: bool = False,
+    num_ctx: int | None = None,
 ) -> AsyncGenerator[ChatChunk, None]:
     """Stream chat completion from Ollama with tool support.
 
@@ -170,7 +194,8 @@ async def stream_chat_with_tools(
     Thinking tokens are consumed by Ollama and not forwarded to the caller;
     only the final response content is yielded. Expect higher TTFT when enabled.
     """
-    options: dict = {"num_ctx": Config.OLLAMA_NUM_CTX}
+    resolved_ctx = num_ctx or Config.OLLAMA_NUM_CTX
+    options: dict = {"num_ctx": resolved_ctx}
     if tools:
         options["num_predict"] = 8192
     payload: dict = {