`tidb_enable_async_merge_global_stats` cannot work correctly

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Bug Report

Please answer these questions before submitting your issue. Thanks!

1. Minimal reproduce step (Required)

1. Start the TiDB with the following code:

diff --git a/pkg/statistics/handle/globalstats/global_stats.go b/pkg/statistics/handle/globalstats/global_stats.go
index 78ee277659..9a814ca4ca 100644
--- a/pkg/statistics/handle/globalstats/global_stats.go
+++ b/pkg/statistics/handle/globalstats/global_stats.go
@@ -103,6 +103,7 @@ func MergePartitionStats2GlobalStats(
        histIDs []int64,
 ) (globalStats *GlobalStats, err error) {
        if sc.GetSessionVars().EnableAsyncMergeGlobalStats {
+               logutil.BgLogger().Info("use async merge global stats", zap.String("table", globalTableInfo.Name.L))
                worker, err := NewAsyncMergePartitionStats2GlobalStats(statsHandle, globalTableInfo, histIDs, is)
                if err != nil {
                        return nil, errors.Trace(err)
@@ -113,6 +114,7 @@ func MergePartitionStats2GlobalStats(
                }
                return worker.Result(), nil
        }
+       logutil.BgLogger().Info("use blocking merge global stats", zap.String("table", globalTableInfo.Name.L))
        return blockingMergePartitionStats2GlobalStats(sc, statsHandle.GPool(), opts, is, globalTableInfo, isIndex, histIDs, nil, statsHandle)
 }

2. Create a database and partitioned table:

CREATE DATABASE IF NOT EXISTS partition_example;
USE partition_example;
CREATE TABLE example_table (
    id INT NOT NULL,
    name VARCHAR(50),
    PRIMARY KEY (id)
)
PARTITION BY RANGE (id) (
    PARTITION p0 VALUES LESS THAN (2),
    PARTITION p1 VALUES LESS THAN (4),
    PARTITION p2 VALUES LESS THAN (6),
    PARTITION p3 VALUES LESS THAN (8),
    PARTITION p4 VALUES LESS THAN MAXVALUE
);

3. Insert 3000 rows:

import { Client } from "https://deno.land/x/mysql/mod.ts";

const client = await new Client().connect({
  hostname: "127.0.0.1",
  port: 4000,
  username: "root",
  db: "partition_example",
  password: "",
});

async function insertData() {
  for (let i = 1; i <= 3000; i++) {
    const name = `Name${i}`;
    await client.execute(`INSERT INTO example_table (id, name) VALUES (?, ?)`, [
      i,
      name,
    ]);
  }
}

await insertData();

await client.close();

console.log("Inserted 3000 rows into example_table");

4. Check the logs.

2. What did you expect to see? (Required)

use async merge global stats

3. What did you see instead (Required)

[2024/06/12 19:38:12.833 +08:00] [INFO] [save.go:221] ["directly update count"] [category=stats] [tableID=109] [results.Count=2993] [count=2993]
[2024/06/12 19:38:12.960 +08:00] [INFO] [analyze.go:744] ["analyze table `partition_example`.`example_table` has finished"] [partition=p4] ["job info"="auto analyze table all columns with 256 buckets, 500 topn, 1 samplerate"] ["start time"=2024/06/12 19:38:12.820 +08:00] ["end time"=2024/06/12 19:38:12.958 +08:00] [cost=137.905ms] ["sample rate reason"="use min(1, 110000/2993) as the sample-rate=1"]
[2024/06/12 19:38:12.963 +08:00] [INFO] [global_stats.go:117] ["use blocking merge global stats"] [table=example_table]

4. What is your TiDB version? (Required)

v7.5.1 with patch