About WEBP or AVIF, when a browser downloads WEBP or AVIF and the file has the extension .jpg, is because the true format of the file was WEBP or AVIF and not JPG, which you can see in Etsy for example, where you can get either webp or avif, but they say it is .jpg.
So Brave Search is not converting anything, it is just giving you the photo URL, either by going to the photo (clicking download) or just copying it.
When you right click and download the file, well, Brave/Chromium is giving you the ‘right format’ regardless of file extension.
Of course you can do what Developers do and rename the file to jpg, if you want.
Using and extension like:
Will truly convert the file, you know, it will be a new file, if you download a file webp, and if you go to devtools and grab the file which will download it as jpg (bypassing the ‘right format’ of Chromium) you will see they have the same HASH which means they are the same file, just with a different extension, if you see their HEX data, you will see it will say WEBP or AVIF inside the file raw data.
But using that extension and saving PNG or JPG, will truly convert, make a new file, probably apply some compression as expected.
Brave Search by default uses WEBP in their image indexer for the thumbnails or previews, but that’s it, that’s grabbing the image from the Brave indexer, which will be different than the original one.
For example a wallpaper 1920x1080 will only be 860x484 when downloaded from Brave indexer preview/thumbnail result page.
So, use the extension, if you want to truly convert and save images to a different format.