Sample Code:

HTML:

<template>
    <lightning-card>
        <lightning-button variant="brand" label="Show Tab 1" onclick={handleClick}></lightning-button>
        <lightning-button variant="brand" label="Show Tab 2" onclick={handleClick}></lightning-button>
        <lightning-button variant="brand" label="Hide Tab 1" onclick={handleClick}></lightning-button>
        <lightning-button variant="brand" label="Hide Tab 2" onclick={handleClick}></lightning-button>
        <lightning-tabset variant="scoped">
            <template if:true={tabOneBool}>
                <lightning-tab label="Item One"> Content for tab 1 </lightning-tab>
            </template>
            <template if:true={tabTwoBool}>
                <lightning-tab label="Item Two"> Content for tab 2 </lightning-tab>
            </template>
        </lightning-tabset>
    </lightning-card>
</template>

JavaScript:

import { LightningElement } from 'lwc';

export default class TabSet extends LightningElement {

    tabOneBool;
    tabTwoBool;

    handleClick( event ) {

        let buttonClicked = event.target.label;

        switch( buttonClicked ) {

            case 'Show Tab 1':
                this.tabOneBool = true;
                break;

            case 'Show Tab 2':
                this.tabTwoBool = true;
                break;

            case 'Hide Tab 1':
                this.tabOneBool = false;
                break;

            case 'Hide Tab 2':
                this.tabTwoBool = false;
                break;
            
        }

    }

}

js-meta.xml:

<?xml version="1.0" encoding="UTF-8"?>
<LightningComponentBundle xmlns="http://soap.sforce.com/2006/04/metadata">
    <apiVersion>52.0</apiVersion>
    <isExposed>true</isExposed>
    <targets>
        <target>lightning__Tab</target>
    </targets>
</LightningComponentBundle>

Output: