Update.
I spoke with an AppleCare advisor. Using screen sharing, he observed me demonstrating process used to edit a photo with PSE 2025 as an External Editor. Open image in Mac Photos > Edit > External Editors > PSE 2025 (to do edit) > File > Save > JPEG Options > OK, and this is where the problem was found. There is no option in PSE 2025 to save the edited photo directly to the Mac Photo app. The option is grayed out in the drop-down window. By default, PSE saves the image to the Pictures file. As a result, the file must be exported to the desktop and then imported into Mac Photos. The image edited in PSE 2025 is saved to the Pictures file rather than saving over the original image in the Mac Photos app.
The next step was to repeat the process using my PSE 2024 version. It worked perfectly to Save Changes in PSE 2024, allowing immediate return to Mac Photos External Editor > Save Changes. One image was saved in Photos app with edits from PSE 2024 applied.
The only way to use the PSE 2025 edited file is to export it to the desktop and import it into Photos. Since this product does not serve my needs, the AppleCare advisor suggested that I contact Adobe Support to report the issue and request a refund.
I called Adobe and had to request to be connected to technical support (no direct line). The advisor I spoke to completely understood the issue and readily agreed to approve a refund for the amount I paid for the upgrade from PSE 2024 to PSE 2025.