logproto: remove handshake_in_progress from LogProtoClient #1357

Job	Run time
create-source-tarball	1m 45s
create-packages / debian-bookworm	6m 1s
create-packages / debian-testing	5m 47s
create-packages / fedora-39	6m 0s
create-packages / ubuntu-jammy	8m 20s
	27m 53s

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