Yes, 0.40.2 seems to work fine on Debian 12.
I had looked briefly, but failed to find the older versions in the itch app. Sorry for missing that.
For anyone else looking:
1. Install the itch app and login
2. Install (the latest version of) "deepdwn-linux.appimage" from your library. You don't get any option to select a version yet; that's fine.
3. Right click on the entry for deepdwn and select "Manage" (or click the gear next to the "Launch" button).
4. Next to the "deepdwn-linux.appimage" item, the button has changed from "Install" to "Manage"; click this new "Manage" button.
5. Click "Switch to another version..."
6. Click on the desired version. The itch app will immediately install this version over the existing one.
7. You can now find the AppImage in the install location (~/.config/itch/apps/deepdwn/) and copy it to (or link to it from) your preferred path.