LFC fixes + statistics (#5727)

## Problem

## Summary of changes

See #5500

## Checklist before requesting a review

- [ ] I have performed a self-review of my code.
- [ ] If it is a core feature, I have added thorough tests.
- [ ] Do we need to implement analytics? if so did you add the relevant
metrics to the dashboard?
- [ ] If this PR requires public announcement, mark it with
/release-notes label and add several sentences in this section.

## Checklist before merging

- [ ] Do not forget to reformat commit message to not include the above
checklist

---------

Co-authored-by: Konstantin Knizhnik <knizhnik@neon.tech>

test_runner/regress/test_local_file_cache.py

@@ -0,0 +1,74 @@
+import os
+import random
+import threading
+import time
+from typing import List
+
+from fixtures.neon_fixtures import NeonEnv
+from fixtures.utils import query_scalar
+
+
+def test_local_file_cache_unlink(neon_simple_env: NeonEnv):
+    env = neon_simple_env
+
+    cache_dir = os.path.join(env.repo_dir, "file_cache")
+    os.mkdir(cache_dir)
+
+    env.neon_cli.create_branch("test_local_file_cache_unlink", "empty")
+
+    endpoint = env.endpoints.create_start(
+        "test_local_file_cache_unlink",
+        config_lines=[
+            "shared_buffers='1MB'",
+            f"neon.file_cache_path='{cache_dir}/file.cache'",
+            "neon.max_file_cache_size='64MB'",
+            "neon.file_cache_size_limit='10MB'",
+        ],
+    )
+
+    cur = endpoint.connect().cursor()
+
+    n_rows = 100000
+    n_threads = 20
+    n_updates_per_thread = 10000
+    n_updates_per_connection = 1000
+    n_total_updates = n_threads * n_updates_per_thread
+
+    cur.execute("CREATE TABLE lfctest (id int4 PRIMARY KEY, n int) WITH (fillfactor=10)")
+    cur.execute(f"INSERT INTO lfctest SELECT g, 1 FROM generate_series(1, {n_rows}) g")
+
+    # Start threads that will perform random UPDATEs. Each UPDATE
+    # increments the counter on the row, so that we can check at the
+    # end that the sum of all the counters match the number of updates
+    # performed (plus the initial 1 on each row).
+    #
+    # Furthermore, each thread will reconnect between every 1000 updates.
+    def run_updates():
+        n_updates_performed = 0
+        conn = endpoint.connect()
+        cur = conn.cursor()
+        for _ in range(n_updates_per_thread):
+            id = random.randint(1, n_rows)
+            cur.execute(f"UPDATE lfctest SET n = n + 1 WHERE id = {id}")
+            n_updates_performed += 1
+            if n_updates_performed % n_updates_per_connection == 0:
+                cur.close()
+                conn.close()
+                conn = endpoint.connect()
+                cur = conn.cursor()
+
+    threads: List[threading.Thread] = []
+    for _i in range(n_threads):
+        thread = threading.Thread(target=run_updates, args=(), daemon=True)
+        thread.start()
+        threads.append(thread)
+
+    time.sleep(5)
+
+    new_cache_dir = os.path.join(env.repo_dir, "file_cache_new")
+    os.rename(cache_dir, new_cache_dir)
+
+    for thread in threads:
+        thread.join()
+
+    assert query_scalar(cur, "SELECT SUM(n) FROM lfctest") == n_total_updates + n_rows