Paste background noise recording into selection

There’s already a plug-in available to help you do that:

(actually it is two plug-ins, one for copying and one for pasting.)

The user documentation for is in that post.
Installation instructions are here: https://manual.audacityteam.org/man/installing_effect_generator_and_analyzer_plug_ins_on_linux.html#nyquist_install
(It’s a “Nyquist Plug-in”)