Backport PR #60454 on branch 2.3.x (String dtype: coerce missing values in indexers for string dtype Index) #21201

Job	Run time
Linux-32-bit	9m 10s
Linux-Musl	11m 35s
python-dev (macOS-13)	36m 6s
python-dev (macOS-14)	13m 56s
python-dev (ubuntu-22.04)	25m 13s
python-dev (windows-latest)	27m 10s
macos-13 actions-310.yaml	35m 44s
macos-13 actions-311.yaml	32m 49s
macos-13 actions-312.yaml	42m 26s
macos-13 actions-39.yaml	38m 1s
macos-14 actions-310.yaml	24m 46s
macos-14 actions-311.yaml	22m 40s
macos-14 actions-312.yaml	23m 5s
macos-14 actions-39.yaml	44m 51s
windows-latest actions-311.yaml	39m 1s
windows-latest actions-312.yaml	43m 19s
windows-latest actions-310.yaml	39m 26s
windows-latest actions-39.yaml	39m 11s
ubuntu-latest actions-310.yaml	32m 4s
Copy-on-Write 3.10 (warnings)	29m 54s
Copy-on-Write 3.10	30m 9s
ubuntu-latest actions-311.yaml	31m 32s
Future infer strings (without pyarrow)	28m 8s
Locale: zh_CN	27m 48s
Copy-on-Write 3.11	30m 13s
Copy-on-Write 3.11 (warnings)	27m 50s
Locale: it_IT	27m 32s
Downstream Compat	5m 47s
Numpy Dev	23m 34s
Pyarrow Nightly	24m 41s
ubuntu-latest actions-312.yaml	34m 53s
Future infer strings	36m 37s
Copy-on-Write 3.12	30m 29s
ubuntu-latest actions-39.yaml	32m 49s
Copy-on-Write 3.9 (warnings)	28m 42s
Minimum Versions	28m 3s
Copy-on-Write 3.9	28m 22s
Pypy	7m 45s
	18h 15m 21s

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