Sample code:

HTML:

<template>
    <div class="slds-box slds-theme--default"> 
        <lightning-button-menu alternative-text="Show menu" variant="border-filled" onselect={handleOnselect} label="Actions">
            <lightning-menu-item value="Account" label="Create Account"></lightning-menu-item>
            <lightning-menu-item value="Contact" label="Create Contact"></lightning-menu-item>
            <lightning-menu-item value="Lead" label="Create Lead"></lightning-menu-item>
            <lightning-menu-item value="Opportunity" label="Create Opportunity"></lightning-menu-item>
        </lightning-button-menu>
    </div>
</template>

JavaScript:

import { LightningElement, api, track } from 'lwc';
import { NavigationMixin } from 'lightning/navigation';

export default class Sample extends NavigationMixin(LightningElement) {
    
    handleOnselect(event) {

        var selectedVal = event.detail.value;
        console.log( 'Selected button is ' + selectedVal );

        this[NavigationMixin.Navigate]({
            type: 'standard__objectPage',
            attributes: {
                objectApiName: selectedVal,
                actionName: 'new'
            }
        });

    }

}

Output: