Improve nodes._check_initialpaths_for_relpath performance (#13448)

Use `Path` facilities to greatly improve performance of `nodes._check_initialpaths_for_relpath` (see #13448 for performance comparison).

Related: #13420, #13413.

---------

Co-authored-by: Bruno Oliveira <bruno@soliv.dev>

Author: sashko1988

AUTHORS

@@ -332,6 +332,7 @@ Nikolay Kondratyev
 Nipunn Koorapati
 Oleg Pidsadnyi
 Oleg Sushchenko
+Oleksandr Zavertniev
 Olga Matoula
 Oliver Bestwalter
 Omar Kohl

changelog/13420.improvement.rst

@@ -0,0 +1 @@
+Improved test collection performance by optimizing path resolution used in ``FSCollector``.

src/_pytest/nodes.py

@@ -38,7 +38,6 @@
 from _pytest.mark.structures import NodeKeywords
 from _pytest.outcomes import fail
 from _pytest.pathlib import absolutepath
-from _pytest.pathlib import commonpath
 from _pytest.stash import Stash
 from _pytest.warning_types import PytestWarning
 
@@ -548,10 +547,13 @@ def _traceback_filter(self, excinfo: ExceptionInfo[BaseException]) -> Traceback:
 def _check_initialpaths_for_relpath(
     initial_paths: frozenset[Path], path: Path
 ) -> str | None:
-    for initial_path in initial_paths:
-        if commonpath(path, initial_path) == initial_path:
-            rel = str(path.relative_to(initial_path))
-            return "" if rel == "." else rel
+    if path in initial_paths:
+        return ""
+
+    for parent in path.parents:
+        if parent in initial_paths:
+            return str(path.relative_to(parent))
+
     return None