sshd forks a new clean process for each connection, so this whole machinery happens each time you connect. Each connection is a full fork/exec, and the backdoor has to set itself up from scratch again, including all the parsing and hooking.
I have looked in the sshd code at https://github.com/openssh/openssh-portable and I cannot find it forking and re-execing _itself_. It forks and execs other commands, of course, and it forks to handle new connections but does not re-exec in those paths that I can see.
If some inetd-like program were listening on port 22 and fork+exec'ing sshd to handle each incoming connection, that would explain it. But on my systemd-based Linux system I see a long-running sshd that appears to be taking care of port 22.
I do agree that it seems like the best explanation of the delay is that somehow sshd was being exec'ed per connection, but I haven't seen all the dots connected yet.
You should also be able to see the error message "sshd re-exec requires execution with an absolute path" in the source. If you follow the `rexec_flag` tested above this message, you can see where it calls execv, later in the code.