[infra] Remove client directory

Change-Id: If4b76234e5b8988faef4ed4df66df7d7d6ec5638
Reviewed-on: https://dart-review.googlesource.com/c/sdk/+/223422
Reviewed-by: William Hesse <[email protected]>
Reviewed-by: Vijay Menon <[email protected]>
Reviewed-by: Devon Carew <[email protected]>
Commit-Queue: Alexander Thomas <[email protected]>

Author: athomas