[Maintenance] Refactor DateTimeInput

[langehm]

Relevant template

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Problem description (optional)

Current implementation depends on using ref of the vuetify components. Furthermore all props are required - this is in congestion with the given example inside the components. This example does not work out of the box.

Desired solution

Make as many props optional and improve the logic in general. Remove the icon for clearing the input. Vuetify offers clearable props.

Considered alternatives (optional)

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Additional context (optional)

Evaluate the UI/UX decision with two input fields directly next to each other.

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