Lightning-quick-action-panel include lightning spinner

As you want to display a spinner, you will need to use the screen action instead of the headless action. Call the apex method(getAccountReport) as soon as the record id is passed down to the component. I don't know why the record id is not present in connectedCallack, so thought of an alternative way to call this from the setter method of the recordId.

Here is the code I tried.

// add your imports here.
export default class GetAccountInfosQALWC extends LightningElement {
    @api
    get recordId() {
        return this._recordId;
    }
    set recordId(value) {
        this._recordId = value;

        if (this._recordId) {
            this.callApex();
        }
    }

    _recordId;
    isLoading = true;

    callApex() {
        getAccountReport({ accId: this.recordId })
            .then((result) => {
                if (result != true && result != "true") {
                    this.showToastMessage(1, result);
                } else {
                    this.showToastMessage(
                        2,
                        "The report was successfully downloaded"
                    );
                    eval("$A.get('e.force:refreshView').fire();");
                }
                // call close quickAction
                this.closeAction();
            })
            .catch((error) => {
                console.log(error);
            })
            .finally(() => {
                this.isLoading = false;
            });
    }

    closeAction() {
        this.dispatchEvent(new CloseActionScreenEvent());
    }
}

Refer to this post: how to close quick action programmatically.

Note: Please note that you will need to remove the action from the page layout in order to change the type of action.

What you can do is call your deletePartnerMembers apex function with .then() & .catch() & do your further processing in then-callback like this-

deletePartnerMembers ({partnerId: self.recordId})
  .then (() => {
    // code to further processing
  })
  .catch (() => {
    //error handling
  });

It'll wait for deletePartnerMembers to get executed completely.