In Salesforce, we can use Screen Action using Lightning Web Component to allow users to select the files to Download Selected Files.

Apex Class:

public with sharing class MassDownloadFilesController {
    
    @AuraEnabled( cacheable = true )
    public static List < FilesWrapper > fetchRelatedFiles( 
        Id strRecordId 
    ) {

        List < FilesWrapper > listFilesWrapper = new List < FilesWrapper >();

        for ( ContentDocumentLink objCDL: [ 
            SELECT ContentDocument.LatestPublishedVersionId,
            ContentDocument.Title
            FROM ContentDocumentLink
            WHERE LinkedEntityId =: strRecordId 
        ] ) {

            listFilesWrapper.add( 
                new FilesWrapper(
                	objCDL.ContentDocument.LatestPublishedVersionId,
                    objCDL.ContentDocument.Title
                )
            );

        }

        return listFilesWrapper;        
        
    }
    
    public class FilesWrapper {
        
        @AuraEnabled
        public Id documentId;
        @AuraEnabled
        public String documentName;
            
        public FilesWrapper( 
            Id documentId, String documentName 
        ) {
            
            this.documentId = documentId;
            this.documentName = documentName;
            
        }
        
    }

}

Sample Lightning Web Component:

HTML:

<template>
    <lightning-quick-action-panel header="Files Download">
        <lightning-datatable
            key-field="documentId"
            data={files}
            columns={columns}
            onrowselection={handleRowSelection}>
        </lightning-datatable>      
        <div slot="footer">
            <lightning-button 
                variant="brand" 
                label="Download Selected File(s)" 
                onclick={downloadFiles}
                class="slds-var-p-around_medium">
            </lightning-button>
            <lightning-button 
                variant="brand" 
                label="Close" 
                onclick={closeQuickActionDialog}
                class="slds-var-p-around_medium">
            </lightning-button>
        </div>
    </lightning-quick-action-panel>
</template>

JavaScript:

import { LightningElement, api, wire } from 'lwc';
import { CloseActionScreenEvent } from 'lightning/actions';
import { ShowToastEvent } from 'lightning/platformShowToastEvent';
import fetchRelatedFiles from '@salesforce/apex/MassDownloadFilesController.fetchRelatedFiles';  
import { NavigationMixin } from 'lightning/navigation';

export default class MassDownloadFiles extends NavigationMixin ( 
    LightningElement 
) {

    @api recordId;
    selectedFileIds = [];
    files = [];
    columns = [  
        { label: 'Name', fieldName: 'documentName' },
    ];  

    @wire( fetchRelatedFiles, {
        strRecordId: '$recordId',
    } )
    wiredRecord( { error, data } ) {   

            if ( data ) {  
                
                console.log( 
                    'data is', 
                    JSON.stringify( data ) 
                );

                if ( data.length > 0 ) {

                    this.files = data;

                } else {

                    this.dispatchEvent(
                        new ShowToastEvent({
                            title: 'File(s) Download',
                            message: 'Check whether File(s) are attached!!!',
                            variant: 'error'
                        }),
                    );

                }
    
            } else if ( error ) {  

                this.dispatchEvent(
                    new ShowToastEvent({
                        title: 'File(s) Download Failed',
                        message: 'System Error Occurred',
                        variant: 'error'
                    }),
                );
    
            } 

    }

    handleRowSelection( event ) {

        const selectedRows = event.detail.selectedRows;
        this.selectedFileIds = [];

        for ( let i = 0; i < selectedRows.length; i++ ) {

            this.selectedFileIds.push( selectedRows[ i ].documentId );

        }

    }

    downloadFiles(){

        let filesDownloadUrl = '/sfc/servlet.shepherd/version/download';

        this.selectedFileIds.forEach( item => {
            filesDownloadUrl += '/' + item
        });

        console.log( 
            'filesDownloadUrl is', 
            filesDownloadUrl 
        );

        this[ NavigationMixin.Navigate ]( {
            type: 'standard__webPage',
            attributes: {
                url: filesDownloadUrl
            }
        }, false );

        this.dispatchEvent(
            new ShowToastEvent( {
                title: 'File(s) Download',
                message: 'File(s) Downloaded Successfully!!!',
                variant: 'success'
            } ),
        );

        /*
            Closing the dialog after 3 seconds
        */
        setTimeout( () => {
            this.closeQuickActionDialog();
        }, 3000 );

    }

    closeQuickActionDialog() {
        
        console.log( 
            'Inside Close Method' 
        );
        this.dispatchEvent( 
            new CloseActionScreenEvent() 
        );

    }

}

js-meta.xml:

<?xml version="1.0" encoding="UTF-8"?>
<LightningComponentBundle xmlns="http://soap.sforce.com/2006/04/metadata">
    <apiVersion>58.0</apiVersion>
	<isExposed>true</isExposed>
	<targets>
		<target>lightning__RecordAction</target>
		<target>lightning__RecordPage</target>
	</targets>
	<targetConfigs>
		<targetConfig targets="lightning__RecordAction">
			<actionType>ScreenAction</actionType>
		</targetConfig>
	</targetConfigs>
</LightningComponentBundle>

Create a Quick Action and add it to the page layout.

Output: