I have been vuetify's <v-tooltip> and I don't find any attributes in their API so I could either use \n or <br /> to create a newline inside the tooltip template.
Exemple :
<v-tooltip>
<template v-slot:activator="{ on }">
<v-btn>
button
</v-btn>
</template>
<span>First line \n second line</span>
</v-tooltip>
This will still display
First line second line
instead of
First line
second line