[backport 2.3.x] BUG: preserve (object) dtype in factorize (#60118) #19951

Job	Run time
Linux-32-bit	19m 55s
Linux-Musl	18m 5s
python-dev (macOS-13)	27m 26s
python-dev (macOS-14)	17m 6s
python-dev (ubuntu-22.04)	24m 32s
python-dev (windows-latest)	27m 21s
macos-13 actions-310.yaml	58m 4s
macos-13 actions-311.yaml	57m 19s
macos-13 actions-312.yaml	55m 52s
macos-13 actions-39.yaml	46m 22s
macos-14 actions-310.yaml	35m 36s
macos-14 actions-311.yaml	29m 13s
macos-14 actions-312.yaml	28m 45s
macos-14 actions-39.yaml	32m 54s
windows-latest actions-311.yaml	53m 12s
windows-latest actions-312.yaml	1h 0m 40s
windows-latest actions-310.yaml	50m 39s
windows-latest actions-39.yaml	39m 23s
ubuntu-latest actions-310.yaml	1h 2m 41s
Copy-on-Write 3.10 (warnings)	39m 0s
Copy-on-Write 3.10	40m 8s
ubuntu-latest actions-311.yaml	58m 57s
Future infer strings (without pyarrow)	59m 15s
Locale: zh_CN	37m 59s
Copy-on-Write 3.11	39m 16s
Copy-on-Write 3.11 (warnings)	37m 15s
Downstream Compat	9m 11s
Locale: it_IT	37m 36s
Numpy Dev	23m 26s
Pyarrow Nightly	23m 45s
Future infer strings	52m 27s
ubuntu-latest actions-312.yaml	46m 15s
Copy-on-Write 3.12	42m 0s
ubuntu-latest actions-39.yaml	49m 29s
Copy-on-Write 3.9	29m 53s
Minimum Versions	29m 25s
Copy-on-Write 3.9 (warnings)	29m 46s
Pypy	7m 52s
	23h 58m 0s

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