Short answer: drop a square image of at least 512 px and download the ZIP. It contains 16/32/48/180/192/512 px PNGs, a real favicon.ico, a web manifest and the head snippet with the paths already matched.
Why the .ico still exists
Modern browsers read PNG icons, but Windows shortcuts, some feed readers and older bookmarks still ask for /favicon.ico. Shipping one real ICO file covers those without a 404 in the logs, and it is the file many crawlers request first.
Keep the source square
Icons are square by definition. A non-square image is centre-cropped, which is right for a logo in a circle and wrong for a wordmark. Pad the source to a square first when the whole mark has to survive.