[lldb] [gdb-remote] Move ReadPacketWithOutputSupport() to client

Move ReadPacketWithOutputSupport() from GDBRemoteCommunication
to GDBRemoteClientBase.  This function is client-specific and moving
it there simplifies followup patches that split communication into
separate thread.

Sponsored by: The FreeBSD Foundation

Differential Revision: https://reviews.llvm.org/D135028