fix(prompts): mirror user's language in reasoning + reply

DeepSeek V4's `reasoning_content` channel inherits the system
prompt's English bias even when users write in Chinese, so the
visible thinking trace stays in English alongside (sometimes
mixed-language) replies.

Adds a `## Language` section near the top of `base.md` directing
the model to mirror the user's language in *both*
`reasoning_content` and the final reply, with a carve-out so
identifiers, file paths, tool names, and log lines stay in their
original form (translating `read_file` to `读取文件` would break
tool calls). Default remains English when no clear signal is
present, so existing behaviour is preserved.

Includes a structural test in `crates/tui/src/prompts.rs` that
asserts the section ships in every mode (Agent / Yolo / Plan).
Wording is intentionally not asserted on, per the existing test
module's "don't fail on prose" comment.

Reported via the project Telegram community (#588).

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

crates/tui/src/prompts.rs

@@ -606,6 +606,20 @@ mod tests {
         assert!(prompt.contains("### `rlm`"));
     }
 
+    /// #588: language-mirroring directive must ship in every mode so
+    /// DeepSeek's `reasoning_content` and final reply follow the user's
+    /// language. Structural test — wording is not a test concern.
+    #[test]
+    fn language_mirroring_section_present_in_all_modes() {
+        for mode in [AppMode::Agent, AppMode::Yolo, AppMode::Plan] {
+            let prompt = compose_prompt(mode, Personality::Calm);
+            assert!(
+                prompt.contains("## Language"),
+                "## Language section missing from mode {mode:?}"
+            );
+        }
+    }
+
     /// #358: rlm guidance was reframed from "first-class" to "specialty
     /// tool" — verify the structural markers are present so a future
     /// change doesn't silently remove the RLM section entirely.

crates/tui/src/prompts/base.md

@@ -1,5 +1,11 @@
 You are DeepSeek TUI. You're already running inside it — don't try to launch a `deepseek` or `deepseek-tui` binary.
 
+## Language
+
+Detect the language the user writes in and respond in that same language — including your internal reasoning. If the user writes in Simplified Chinese (简体中文), your `reasoning_content` and final reply must both be in Simplified Chinese. If they switch languages mid-conversation, switch with them. The default when no clear signal is present is English.
+
+Code, file paths, identifiers, tool names, and log lines stay in their original form — translating `read_file` to `读取文件` would break tool calls. Only natural-language prose mirrors the user.
+
 ## Preamble Rhythm
 
 When starting work on a user request, open with a short, momentum-building line that names the action you're taking. Keep it reserved — state what you're doing, not how you feel about it.