Using the v-html tag raw HTML can be displayed in a component. This HTML can be stored in a database and displayed at run-time. However you cannot use vue syntax.
The v3-runtime-template plugin allows the use of vue syntax in a template installed at run-time. Note this requires that Vue Build includes the Vue Compiler.
The template displayed as part of the page
The Cyan Box is a run-time template stored in a database & displayed as part of this page.
This run-time template references 2 name variables, a computed value & a function all declared on the parent page.
Change the template content in real-time
This is the run-time template displayed as inputs.
You can alter this template & watch what happens to the template output. If you render the HTML invalid you will be shown the valid HTML, otherwise the cyan template will change reflecting the changes you have made:

Here is the 'family name' variable which you can alter:
Jones