[SalesForce] Refresh Standard Related List from LWC

I had this issue myself today as well. In my case, I had a Quick Action Lightning Aura Component which enveloped a Lightning Web Component (because there is currently no way of using a Lightning Web Component as a Quick Action)..

What I did is set up my Aura Component to catch 'close' events:

<!-- aura/auraComponent/auraComponent.cmp -->
<aura:component implements="force:lightningQuickAction,force:hasRecordId">
    <c:webComponent recordId="{!v.recordId}" onclose="{!c.handleClose}" />
</aura:component>

And process them with the events I would LIKE to throw from my Web Component:

// aura/auraComponent/auraComponentController.js
({
    handleClose: function() {
        $A.get('e.force:refreshView').fire();
        $A.get("e.force:closeQuickAction").fire();
    }
})

And in my Web Component I throw the following Custom Event to trigger the refresh & quick action close:

this.dispatchEvent(new CustomEvent('close'));

I know it's ugly, but at the time of writing I don't think there's a better way to refresh an underlying record page & close a Quick Action modal from a Lightning Web Component.

The issue you are having is with how you are saving the response value you get back from the wire method. you are capturing it as a generic object {data,error} however you aren't saving that to a variable external from the wire method. In order to use RefreshApex you have to pass in the response you get back from the wire method like below.

    @track oppResponse;

    @wire(getOppList, { groupLabel: '$profileGroup', recordId: '$recordId' })
                wiredFlows(response) {
                    this.oppResponse = response;
                    let data = response.data;
                    let error = response.error;
                    if (data) {
                        this.error = undefined;
                        this.outputData = data;
                    } else if (error) {
                        this.error = error;
                        this.outputData = undefined;
                    }
                }
     @api forceRefreshInitiated() {
                refreshApex(this.oppResponse);
            }