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What you could do is use ternary operator to switch between connected and not connected text based on status as so instead of using v-if(if used needs else span also and your status should be of type string and null as per your given code,if not string then just use v-if="status" and v-else):
<div class="api_data">
<span class="trick_ok">{{this.status=='connected'?'Connected':'Not connected'}}</span>
</div>
Source:stackexchange.com