Hello @Thomas Schrattenecker
Welcome to the Atlassian Community!
There are no default workflow templates in Jira for web design process, however, since Jira workflows are completely customizable, you can create a customized workflow that would properly address your current scenario.
You can check in the links below some examples and tips to customize your workflow to the web design process:
JIRA Workflow for Web Development Example: Simple and Effective
Using JIRA Software for Web Design and Development?
Let us know If you have any specific questions about Jira workflows to properly achieve your goals.
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