The below is a work in progress. Don't be surprised if there are quirks in the information provided below. PRs are welcome.
KiTTY has an auto reconnect option, but it's not fast enough to catch the first few messages
There's a Kconfig setting to delay starting the logging thread.
Set it a tad higher, should let you catch first log messages.
LOG_PROCESS_THREAD_STARTUP_DELAY_MS is the setting.