Enhance logging and timing in CLI and session operations

- Updated the `_print_checks` function to replace console prints with logging functions for better traceability.
- Introduced timing functionality in the `doctor`, `dry_run`, and `up` functions to log the duration of preflight checks.
- Modified the `wait_ssh` function to accept a logging callback, improving SSH wait feedback.
- Enhanced the `mark` method in `PhaseTimes` to log phase durations, aiding in performance analysis.
- Updated various remote scripts to ensure error messages are printed to stderr for better error handling.

tests/test_timing.py

@@ -1,4 +1,11 @@
-from gpu_rent.timing import PhaseTimes, WaitLog, format_duration
+from gpu_rent.timing import (
+    PhaseTimes,
+    WaitLog,
+    clock_elapsed,
+    clock_prefix,
+    clock_reset,
+    format_duration,
+)
 
 
 def test_format_duration():
@@ -20,6 +27,36 @@ def test_phase_times_summary(monkeypatch):
     assert "всего" in line
 
 
+def test_phase_times_mark_logs(monkeypatch):
+    times = iter([0.0, 45.0])
+    monkeypatch.setattr("gpu_rent.timing.time.monotonic", lambda: next(times))
+    logs: list[str] = []
+    clock = PhaseTimes()
+    clock.mark("SSH", logs.append)
+    assert logs == ["фаза SSH: 45s · всего 45s"]
+
+
+def test_phase_summary_lines_annotate_long_work(monkeypatch):
+    # t0=0, mark provision at 120s
+    times = iter([0.0, 120.0, 120.0])
+    monkeypatch.setattr("gpu_rent.timing.time.monotonic", lambda: next(times))
+    clock = PhaseTimes()
+    clock.mark("provision")
+    lines = clock.summary_lines()
+    assert lines[0] == "тайминг up:"
+    assert any("provision" in ln and "оптимизировать?" in ln for ln in lines)
+    assert any("seed/extensions/LLM" in ln for ln in lines)
+
+
+def test_phase_summary_lines_annotate_wait(monkeypatch):
+    times = iter([0.0, 40.0, 40.0])
+    monkeypatch.setattr("gpu_rent.timing.time.monotonic", lambda: next(times))
+    clock = PhaseTimes()
+    clock.mark("SSH")
+    lines = clock.summary_lines()
+    assert any("SSH" in ln and "ожидание" in ln for ln in lines)
+
+
 def test_wait_log_throttles(monkeypatch):
     logs: list[str] = []
     t = {"now": 0.0}
@@ -31,3 +68,13 @@ def test_wait_log_throttles(monkeypatch):
     t["now"] = 31.0
     w.tick("c")
     assert logs == ["a", "c"]
+
+
+def test_clock_prefix(monkeypatch):
+    t = {"now": 100.0}
+    monkeypatch.setattr("gpu_rent.timing.time.monotonic", lambda: t["now"])
+    clock_reset()
+    assert clock_prefix() == "[+0s] "
+    t["now"] = 112.0
+    assert clock_prefix() == "[+12s] "
+    assert clock_elapsed() == 12.0