[SalesForce] alternative for WorkspaceApi in LWC

e.force:navigateToComponent is deprecated. I wont recommend using it.

Instead use lightning:navigation , you generate state(aka URL params) by setting page references.

<lightning:navigation aura:id="navService"/>

JS:

 var navService = cmp.find("navService");
    // Sets the route to /lightning/o/Account/home
    var pageReference = {
        type: 'standard__component',
        attributes: {
            componentName: 'c:testContainer'
        },
        state : {
            c__recordId : cmp.get('v.recordId');
        }
    };

    // Set the URL on the link or use the default if there's an error
    var defaultUrl = "#";
    navService.generateUrl(pageReference).then($A.getCallback(function(url) {
        window.open(url,'_blank'); // This will open in new tab with pageReference with state/URL params you sent while creating instance of pageReference
    }

In your client-side aura controller, set the pageReference attribute for the Component . Set the URL on your link using the generateUrl() method, which is useful for opening links in a new tab

Now you have to make your LWC component listen to pageReference and get state(the recordId that we sent)

you can do that in your lwc by declaing @wire(CurrentPageReference)

import { CurrentPageReference } from 'lightning/navigation';

export default class TestLWC {


     // Injects the page reference that describes the current page
    @wire(CurrentPageReference)
    currentPageReference; 

    get recordIdFromState(){
        return this.currentPageReference &&
            this.currentPageReference.state.c__recordId; // Once you have recordId you can call apex
    }
}

First check if you are in lightning or classic. If in lightning, use navigation.mixin. If in classic, use window.location.assign().

if(document.referrer.indexOf(".lightning.force.com") > 0){
            this[NavigationMixin.Navigate]({
                type: 'standard__recordPage',
                attributes: {
                    recordId: this.record.id,
                    actionName: 'view'
                }
            });
        }else{
            window.location.assign('/'+this.record.id);
        }