More thoroughly type `RemoteHandle` #1042

Job	Run time
wheel-cpp-build / compute-matrix	2s
checks / other-checks	30s
checks / check-style	1m 2s
changed-files / Check changed files	5s
devcontainer / build (amd64, 12.5, conda)	2m 33s
devcontainer / build (amd64, 12.5, pip)	2m 19s
wheel-cpp-build / 11.8.0, 3.12, amd64, rockylinux8	1m 8s
wheel-cpp-build / 12.5.1, 3.12, amd64, rockylinux8	1m 18s
wheel-cpp-build / 11.8.0, 3.12, arm64, rockylinux8	2m 27s
wheel-cpp-build / 12.5.1, 3.12, arm64, rockylinux8	2m 6s
conda-cpp-build	0s
conda-python-build	0s
conda-cpp-tests	0s
docs-build	0s
conda-python-tests	0s
wheel-python-build	1s
wheel-python-tests	1s
pr-builder / run	1s
	13m 33s

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