We chose to label the input "URL" to clarify that the tool is not limited to packages. The form does accept full URLs but the schema and host are trimmed from the input box once they are submitted. On second look that may be somewhat misleading.
It could be a better experience to keep the full URL in the input box after the badge is created OR to label the input something like Path and clarify that it can be any pkg.go.dev URL path and is not limited to packages. I think in any case we should accept full URL or a pkg.go.dev path as input.