Can I retrieve the sketch that is currently loaded on my Uno?

I recently asked Can I determine which sketch is currently loaded on my Uno?

The crux seems to be having access to the binary flashed into the Uno. Is there some way to retrieve what is actually loaded? Can the entirety be sucked back out somehow?

Yes. Look up AVRDUDE.

I also mentioned avrdude and other keywords to google in your previous post

If you turn on verbose output during upload in File > Preferences, you can do an upload and then check the contents of the black console window at the bottom of the Arduino IDE window to see the avrdude command generated by the Arduino IDE. It doesn't matter if the command fails. Make sure not to actually upload to your board, otherwise you'll lose the sketch you're trying to download! Now you just need to make a small adjustment to that command to make it read instead of write. For example, say your upload command is something like this:

C:\Users\per\AppData\Local\Arduino15\packages\arduino\tools\avrdude\6.3.0-arduino14/bin/avrdude -CC:\Users\per\AppData\Local\Arduino15\packages\arduino\tools\avrdude\6.3.0-arduino14/etc/avrdude.conf -v -patmega328p -carduino -PCOM6 -b115200 -D -Uflash:w:C:\Users\per\AppData\Local\Temp\arduino_build_779332/sketch_dec18a.ino.hex:i

You would run this command from the command line:

C:\Users\per\AppData\Local\Arduino15\packages\arduino\tools\avrdude\6.3.0-arduino14/bin/avrdude -CC:\Users\per\AppData\Local\Arduino15\packages\arduino\tools\avrdude\6.3.0-arduino14/etc/avrdude.conf -v -patmega328p -carduino -PCOM6 -b115200 -D -Uflash:r:downloaded.hex:i

The only differences are changing the flash operation from w (write) to r (read) and specifying the filename you want the download to be saved as on your computer (in this case I arbitrarily chose "downloaded.hex").

Reference: https://www.nongnu.org/avrdude/user-manual/avrdude_4.html#Option-Descriptions