How to include GDB commands in logging file?

This is the subject of GDB feature request, which is at least 12 years old :-(

There is currently no way to achieve this. You may use script to record the entire GDB session, but that has a distinct disadvantage of also recording various screen control "garbage" characters.

I don't know when it was introduced, but @prasannatsm presents the solution here): set trace-commands on.

I'd just like to add upon that and show the full process. Here's how I like to start logging now:

set logging file ~/temp/gdb.txt
set logging on
set trace-commands on
show logging
flush

show logging at the end is just to verify everything is logging and working as-expected.

Notice that set trace-commands on causes each command you type to be echoed back out to you now (and also logged if logging is on) with a + preceding it to show it was an echoed command input, not the response.

This can be seen in the output here, for instance:

+show logging
Currently logging to "/home/gabriel.staples/temp/gdb.txt".
Logs will be appended to the log file.
Output will be logged and displayed.
+flush
Register cache flushed.

set trace-commands on: echos the command in screen before executing it. Use this along with logging to get the command written to file.