As you have already discovered, that won’t work because the Webpage Card’s url option expects a string value representing the URL.
input_text.mealie_url is not a URL. It’s the entity_id of an Input Text whose state value contains your URL. The Webpage Card doesn’t support getting the state value of an Input Text (or any other helper).
If the url option supported a template, then we would have a way of getting an Input Text’s state value. However, it doesn’t so you can’t use a Webpage Card the way you intended.
You can investigate the use of Custom Card -Templater. Someone else had a need for making the Webpage Card’s url option support templates (so it can dynamically compute the URL) and they used Card-Templater to do it. No guarantees it’ll meet all your requirements but it’s worth trying.
After you install Card-Templater, try something like this:
type: custom:card-templater
card:
type: iframe
url_template: "{{ states('input_text.mealie_url') }}"
aspect_ratio: 50%
entities:
- entity: input_text.mealie_url