Using NavigationMixin.Navigate with type: ‘standard__recordRelationshipPage’, we achieve Related List View All link behaviour using Salesforce Lightning Web Component(LWC).

Sample Code:

HTML:

<template>
    <lightning-card>
        <lightning-button
            label="View Contacts"
            onclick={viewContacts}>
        </lightning-button><br/><br/>
        <lightning-button
            label="View Opportunities"
            onclick={viewOpptys}>
        </lightning-button><br/><br/>
        <lightning-button
            label="View Cases"
            onclick={viewCases}>
        </lightning-button>
    </lightning-card>
</template>

JavaScript:

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

export default class CustomRelatedLists extends NavigationMixin( LightningElement ) {

    @api recordId;

    viewContacts() {
       
        this[ NavigationMixin.Navigate ]( {
            type: 'standard__recordRelationshipPage',
            attributes: {
                recordId: this.recordId,
                objectApiName: 'Account',
                relationshipApiName: 'Contacts',
                actionName: 'view'
            }
        } );

    }

    viewOpptys() {
       
        this[ NavigationMixin.Navigate ]( {
            type: 'standard__recordRelationshipPage',
            attributes: {
                recordId: this.recordId,
                objectApiName: 'Account',
                relationshipApiName: 'Opportunities',
                actionName: 'view'
            }
        } );

    }

    viewCases() {
       
        this[ NavigationMixin.Navigate ]( {
            type: 'standard__recordRelationshipPage',
            attributes: {
                recordId: this.recordId,
                objectApiName: 'Account',
                relationshipApiName: 'Cases',
                actionName: 'view'
            }
        } );

    }

}

JS-meta.xml:

<?xml version="1.0" encoding="UTF-8"?>
<LightningComponentBundle xmlns="http://soap.sforce.com/2006/04/metadata">
    <apiVersion>55.0</apiVersion>
    <isExposed>true</isExposed> 
    <targets> 
        <target>lightning__RecordPage</target> 
    </targets> 
</LightningComponentBundle>

Output: