does the polarity graphic on this adapter (same as mine) indicate the polarity?
Yes, but it shows both, so I'm not sure why it's printed there.
From your updated pics, it looks like it's inserted as center-positive (aka tip-positive), which is more common IMO. So you just need to find a 12Vdc supply with the correct size of barrel connector which is center-positive polarity (or one that's reversible) and rated for 110 or 120Vac input. Check this wikipedia page to help you measure the size of the DC barrel connector.
If you buy something like this, you should have all options available to you: https://www.amazon.com/Belker-Adapter-Charger-Supply-Electronics/dp/B08ZRVYSGX/ref=sr_1_11?crid=PXOMYJKDG1YI&keywords=12v+supply&qid=1672976034&sprefix=12v+su%2Caps%2C517&sr=8-11