refactor: split core/ui/apps targets and add unit tests

Move all business logic into liblivecaption_core (no Qt dependency) and
the widgets into liblivecaption_ui, leaving two executables: the caption
window and the CLI, which no longer links Qt Widgets. Abstract the ASR
backend behind IAsr so the streaming policy and the live pipeline can be
tested with a scripted fake backend instead of a real model.

把全部业务逻辑下沉到不依赖 Qt 的 liblivecaption_core，界面独立成
liblivecaption_ui，拆出悬浮窗与命令行两个可执行程序（CLI 不再链接 Qt
Widgets）；并用 IAsr 抽象推理后端，使流式策略与实时管线可脱离真模型
用假实现做单元测试。测试还抓到一个真 bug：段恰好结束在 chunk 边界时
只提交了稳定部分，最后几个词被丢掉，已修。

tests/tst_vad.cpp

@@ -0,0 +1,83 @@
+#include <QtTest>
+
+#include <cmath>
+#include <vector>
+
+#include "vad.h"
+
+namespace {
+
+constexpr size_t kFrame = 320;   // 20ms @16k
+constexpr double kPi    = 3.14159265358979323846;
+
+// 生成 amplitude 幅值的 440Hz 正弦，用来模拟"有内容"的音频
+std::vector<float> tone(size_t samples, float amplitude)
+{
+    std::vector<float> v(samples);
+    for (size_t i = 0; i < samples; ++i) {
+        v[i] = amplitude * (float) std::sin(2.0 * kPi * 440.0 * (double) i / 16000.0);
+    }
+    return v;
+}
+
+int countSpeech(lc::Vad & vad, const std::vector<float> & audio)
+{
+    int speech = 0;
+    for (size_t off = 0; off + kFrame <= audio.size(); off += kFrame) {
+        if (vad.feed(audio.data() + off, kFrame)) ++speech;
+    }
+    return speech;
+}
+
+} // namespace
+
+// VAD 的回归测试。
+//
+// 关键教训：噪声底必须用"最小值跟踪"。曾经用均值跟踪，遇到本来就很轻的音频
+// （峰值 RMS 只有 0.03 量级的录音）会把阈值抬到语音电平之上，把绝大部分话音
+// 判成静音 —— 实时字幕于是每句都被切断。
+class TstVad : public QObject {
+    Q_OBJECT
+
+private slots:
+    void backgroundStaysSilent()
+    {
+        lc::Vad vad;
+        const auto bg = tone(kFrame * 200, 0.001f);   // rms ≈ 0.0007
+        QCOMPARE(countSpeech(vad, bg), 0);
+    }
+
+    // 轻语音必须被判成语音：这里语音 rms ≈ 0.0028，
+    // 旧的"均值跟踪 + 0.004 绝对下限"实现会全部漏掉。
+    void quietSpeechIsDetected()
+    {
+        lc::Vad vad;
+        const auto bg = tone(kFrame * 40, 0.001f);    // rms ≈ 0.0007
+        countSpeech(vad, bg);
+
+        const auto sp = tone(kFrame * 100, 0.004f);   // rms ≈ 0.0028
+        const int speech = countSpeech(vad, sp);
+        QVERIFY2(speech >= 95,
+                 qPrintable(QString("轻语音只被识别出 %1/100 帧").arg(speech)));
+    }
+
+    void loudSpeechIsDetected()
+    {
+        lc::Vad vad;
+        const auto sp = tone(kFrame * 50, 0.2f);
+        QVERIFY(countSpeech(vad, sp) >= 48);
+    }
+
+    void floorFollowsQuietInput()
+    {
+        lc::Vad vad;
+        const auto bg = tone(kFrame * 200, 0.001f);
+        countSpeech(vad, bg);
+        // 噪声底应该已经下探到背景噪声量级，而不是停在初值
+        QVERIFY2(vad.noiseFloor() < 0.002f,
+                 qPrintable(QString("噪声底仍为 %1").arg(vad.noiseFloor())));
+    }
+};
+
+QTEST_MAIN(TstVad)
+#include "tst_vad.moc"