More thoroughly type `RemoteHandle` #1036

Job	Run time
changed-files / Check changed files	11s
checks / other-checks	33s
devcontainer / build (amd64, 12.5, conda)	2m 57s
checks / check-style	2m 16s
devcontainer / build (amd64, 12.5, pip)	4m 44s
wheel-cpp-build / compute-matrix	2s
wheel-cpp-build / 11.8.0, 3.12, amd64, rockylinux8	2m 44s
wheel-cpp-build / 12.5.1, 3.12, amd64, rockylinux8	4m 6s
wheel-cpp-build / 11.8.0, 3.12, arm64, rockylinux8	3m 19s
wheel-cpp-build / 12.5.1, 3.12, arm64, rockylinux8	3m 18s
conda-cpp-build	0s
conda-python-build	0s
conda-cpp-tests	0s
conda-python-tests	0s
docs-build	0s
wheel-python-build	1s
wheel-python-tests	1s
pr-builder / run	1s
	24m 13s

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