Change `eltype` methods for objects to types #16814

Job	Run time
doctest (1.10, ubuntu-latest)	24m 47s
doctest (1.11-nightly, ubuntu-latest)	24m 37s
test (1.6, short, ubuntu-latest)	13m 29s
doctest (nightly, ubuntu-latest)	24m 34s
test (1.6, long, ubuntu-latest)	24m 37s
doctest (1.10, ubuntu-latest, depwarn=error)	24m 43s
test (1.10, short, ubuntu-latest)	10m 17s
doctest (1.10, macOS, RPTU)	11m 44s
test (1.10, long, ubuntu-latest)	24m 35s
test (1.11-nightly, short, ubuntu-latest)	17m 53s
test (1.11-nightly, long, ubuntu-latest)	24m 43s
test (nightly, short, ubuntu-latest)	16m 44s
test (nightly, long, ubuntu-latest)	24m 34s
test (1.10, short, ubuntu-latest, depwarn=error)	10m 43s
test (1.10, long, ubuntu-latest, depwarn=error)	24m 33s
test (1.10, short, macOS, RPTU)	5m 35s
test (1.10, long, macOS, RPTU)	14m 17s
test (1.10, book, ubuntu-latest)	24m 33s
test (nightly, book, ubuntu-latest)	24m 35s
	6h 11m 33s

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