logproto: remove handshake_in_progress from LogProtoClient #1358

Job	Run time
create-source-tarball	1m 45s
create-packages / debian-bookworm	6m 16s
create-packages / debian-testing	5m 57s
create-packages / fedora-39	6m 17s
create-packages / ubuntu-jammy	7m 16s
	27m 31s

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