kvserver: replace the use of client_test code with TestCluster/TestSe…

…rver in client_split test

Fixes #50809
Makes progress on #8299

multiTestContext and test store code in client_test are deprecated in favor of running
tests via TestClusteri/TestServer. This is one PR out of many to remove the usage of
multiTestContext in the client_split test cases. This does not remove
all the usages of mtc in this file and just focuses on the simple ones.
The more complex cases that rely on lease expiration will be tackled in a future PR.

Release note: None