You have visual force and inside this your loading the LWC component using Lightning Out in Salesforce Classic Console.
Now,if you want to open a new sub tab (record detail page or visual force page) inside the console on click of a link (inside your LWC .html file) please use the below code.
test.html
<template>
<lightning-card title="Additional Details" icon-name="custom:custom18">
<template if:true={showform}>
<a href="javascript:srcUp('/apex/PageName?id=3773737');" target="_blank">Test</a>
</template>
</lightning-card>
</template>
If it's not working or getting any issue please include the below 2 lines script files in your visual force page.
<apex:includeScript value="/soap/ajax/45.0/connection.js" />
<apex:includeScript value="/support/console/45.0/integration.js" />
Hope this helps you..Enjoy..!