fix: Cleanup `ResourcePool` & Include Mutex Lock for `refreshPool`

[rMaxiQp]

Description

This PR cleans up the resource leakage from TestReopen and TestShrink, which causes flaky tests across ./go/pools/resource_pool_test.go. During my local run, TestIdleTimeout ended up failing with

    resource_pool_test.go:407: 
                Error Trace:    /home/zq2/vitess/go/pools/resource_pool_test.go:407
                Error:          Not equal: 
                                expected: int(2)
                                actual  : int64(6)
                Test:           TestIdleTimeout

Properly closing the resource pool helped to resolve the first issue but surfaces data race from refreshPool:

WARNING: DATA RACE
Write at 0x00c0000b9e68 by goroutine 38:
  runtime.racewrite()
      <autogenerated>:1 +0x1e
  vitess.io/vitess/go/pools.(*poolRefresh).stop()
      /home/zq2/vitess/go/pools/refresh_pool.go:98 +0xc6
  vitess.io/vitess/go/pools.(*ResourcePool).Close()
      /home/zq2/vitess/go/pools/resource_pool.go:147 +0x7e
  vitess.io/vitess/go/pools.TestReopen()
      /home/zq2/vitess/go/pools/resource_pool_test.go:369 +0x30b
  testing.tRunner()
      /usr/local/go/src/testing/testing.go:1934 +0x21c
  testing.(*T).Run.gowrap1()
      /usr/local/go/src/testing/testing.go:1997 +0x44

Previous read at 0x00c0000b9e68 by goroutine 42:
  runtime.raceread()
      <autogenerated>:1 +0x1e
  vitess.io/vitess/go/pools.(*poolRefresh).startRefreshTicker()
      /home/zq2/vitess/go/pools/refresh_pool.go:71 +0xf9
  vitess.io/vitess/go/pools.(*ResourcePool).reopen()
      /home/zq2/vitess/go/pools/resource_pool.go:185 +0x258
  vitess.io/vitess/go/pools.(*poolRefresh).startRefreshTicker.func1.gowrap2()
      /home/zq2/vitess/go/pools/refresh_pool.go:82 +0x42
...

Thus, a mutex lock for refreshPool.go is included here as well.

Related Issue(s)

related to #18965

Checklist

• [ ] "Backport to:" labels have been added if this change should be back-ported to release branches
• [ ] If this change is to be back-ported to previous releases, a justification is included in the PR description
• [ ] Tests were added or are not required
• [ ] Did the new or modified tests pass consistently locally and on CI?
• [ ] Documentation was added or is not required

Deployment Notes

AI Disclosure

This PR was written with the help of Claude Sonnet 4.5

[vitess-bot[bot]]

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