Update `NuGet.Client` from `6.9.1.3` to `6.10.0.100` #23347

Job	Run time
ci (bundler, bundler1, bundler)	8s
ci (bundler, bundler2, bundler)	7s
Lint	1m 5s
ci (cargo, cargo, cargo)	8s
Updater	2m 16s
ci (common, common, common)	50s
ci (composer, composer, composer)	9s
integration	3m 15s
ci (docker, docker, docker)	8s
ci (elm, elm, elm)	9s
ci (git_submodules, git_submodules, gitsubmodule)	8s
ci (github_actions, github_actions, github-actions)	9s
ci (go_modules, go_module, gomod)	9s
ci (gradle, gradle, gradle)	13s
ci (hex, hex, mix)	13s
ci (maven, maven, maven)	13s
ci (npm_and_yarn, npm_and_yarn, npm)	8s
ci (nuget, nuget, nuget)	12m 52s
ci (pub, pub, pub)	10s
ci (python, python, pip)	7s
ci (python, python_slow, pip)	8s
ci (swift, swift, swift)	9s
ci (devcontainers, devcontainers, devcontainers)	8s
ci (terraform, terraform, terraform)	9s
	23m 11s

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