In Salesforce, we can use Quick Action using Lightning Aura Component to allow users to select the files and download the 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;
            
        }
        
    }

}

Lightning Aura Component:

Component:

<aura:component 
                implements="force:lightningQuickAction,force:hasRecordId"
                controller="MassDownloadFilesController">
    <aura:attribute name="filesList" type="List"/>
    <aura:attribute name="mycolumns" type="List"/>
    <aura:attribute name="selectedFileIds" type="String[]"/>
    <lightning:navigation aura:id="navService"/>
    <aura:handler name="init" value="{!this}" action="{!c.fetchFiles}"/>
    <lightning:card>
        <lightning:datatable data="{!v.filesList}" 
                             columns="{!v.mycolumns}" 
                             keyField="documentId"
                             onrowselection="{!c.getSelectedName}"/>
        <aura:set attribute="footer">
            <lightning:button 
                              label="Download Selected File(s)"
                              class="slds-var-p-around_medium"
                              variant="brand"
                              onclick="{!c.downloadFiles}">
            </lightning:button>
        </aura:set>
    </lightning:card>
</aura:component>

JavaScript:

({
    
    fetchFiles : function( 
        component, event, helper 
    ) {
        
        component.set( 'v.mycolumns', [
            { label: 'Name', fieldName: 'documentName', type: 'text' }
        ] );
        let action = component.get( "c.fetchRelatedFiles" );
        action.setParams({
            strRecordId : component.get( "v.recordId" )
        });
        action.setCallback(this, function(response){
            let state = response.getState();
            if (state === "SUCCESS") {
                component.set(
                    "v.filesList", response.getReturnValue()
                );
            }
        });
        $A.enqueueAction(action);
        
    },
    
    getSelectedName: function ( 
        component, event
    ) {
        
        let selectedRows = event.getParam(
            'selectedRows'
        );
        let selectedIds = [];
        for ( let i = 0; i < selectedRows.length; i++ ) {
            
            selectedIds.push(
                selectedRows[ i ].documentId
            );
        }
        
        component.set(
            "v.selectedFileIds",
            selectedIds
        );
        
    },
    
    downloadFiles : function( component ) {      
                
        let selectedFiles = component.get(
            "v.selectedFileIds"
        );
        console.log(
            'selectedFiles are',
            JSON.stringify( selectedFiles )
        );
        
        if ( selectedFiles.length > 0 ) {
            
            let navService = component.find(
                "navService"
            );
            let filesDownloadUrl = '/sfc/servlet.shepherd/version/download';
            
            for ( let item of selectedFiles ) {
                filesDownloadUrl += '/' + item;
            }     
            
            console.log( 
                'filesDownloadUrl is', 
                filesDownloadUrl 
            );  
            let pageReference = {
                type: 'standard__webPage',
                attributes: {
                    url: filesDownloadUrl
                }
            };
            navService.navigate(
                pageReference
            );
            let showToast = $A.get( 
                "e.force:showToast" 
            );
            showToast.setParams({
                title : 'File(s) Download',
                type : 'success',
                mode : 'sticky',
                message : 'File(s) Downloaded Successfully!!!'
            });
            showToast.fire(); 
            
        } else {
            
            let showToast = $A.get( 
                "e.force:showToast" 
            );
            showToast.setParams({
                title : 'File(s) Download',
                type : 'error',
                mode : 'sticky',
                message : 'Please select File(s)'
            });
            showToast.fire(); 
            
        }
        
    }
    
})

Quick Action:

Output: