[tzdb] Replace shared_mutex with mutex. (#87929)

The overhead of taking a std::mutex is much lower than taking a reader
lock on a shared mutex, even under heavy contention.

The benefit of shared_mutex only occurs as the amount of
time spent in the critical sections grows large enough.

In our case all we do is read a pointer and return the lock.
As a result, using a shared lock can be ~50%-100% slower

Here are the results for the provided benchmark on my machine:

```
2024-04-07T12:48:51-04:00
Running ./libcxx/benchmarks/shared_mutex_vs_mutex.libcxx.out
Run on (12 X 400 MHz CPU s)
CPU Caches:
  L1 Data 32 KiB (x6)
  L1 Instruction 32 KiB (x6)
  L2 Unified 1024 KiB (x6)
  L3 Unified 32768 KiB (x1)
Load Average: 2.70, 2.70, 1.63
---------------------------------------------------------------------
Benchmark                           Time             CPU   Iterations
---------------------------------------------------------------------
BM_shared_mutex/threads:1        13.9 ns         13.9 ns     50533700
BM_shared_mutex/threads:2        34.5 ns         68.9 ns      9957784
BM_shared_mutex/threads:4        38.4 ns          137 ns      4987772
BM_shared_mutex/threads:8        51.1 ns          358 ns      1974160
BM_shared_mutex/threads:32       57.1 ns          682 ns      1043648
BM_mutex/threads:1               5.54 ns         5.53 ns    125867422
BM_mutex/threads:2               15.5 ns         30.9 ns     21830116
BM_mutex/threads:4               15.4 ns         57.2 ns     12136920
BM_mutex/threads:8               19.3 ns          140 ns      4997080
BM_mutex/threads:32              20.8 ns          252 ns      2859808
```

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