@api invoke() and uiRecordApi can be used in the Salesforce Lightning Web Component for updating record via Quick Action. 

lightning__RecordAction should be used in the Lightning Web Component to use it in the Quick Action.

Sample Lightning Web Component:

HTML:

<template>    
</template>

JavaScript:

import { LightningElement, api } from 'lwc';
import { updateRecord } from 'lightning/uiRecordApi';
import { ShowToastEvent } from 'lightning/platformShowToastEvent';
import DESCRIPTION_FIELD from '@salesforce/schema/Account.Description';
import ID_FIELD from '@salesforce/schema/Account.Id';

export default class AccountUpdateAction extends LightningElement {

    @api recordId;

    @api invoke() {

        console.log( "Inside Invoke Method" );
        console.log( "Record Id is " + this.recordId );

        const fields = {};
        fields[ ID_FIELD.fieldApiName ] = this.recordId;
        fields[ DESCRIPTION_FIELD.fieldApiName] = 'Testing LWC Quick Action';

        const recordInput = { fields };

        updateRecord( recordInput )
        .then( () => {
            this.dispatchEvent(
                new ShowToastEvent( {
                    title: 'Success',
                    message: 'Account updated',
                    variant: 'success'
                } )
            );
        }).catch( error => {
            this.dispatchEvent(
                new ShowToastEvent( {
                    title: 'Error updating or reloading record',
                    message: error.body.message,
                    variant: 'error'
                } )
            );
        });

    }

}

js-meta.xml:

<?xml version="1.0" encoding="UTF-8"?>
<LightningComponentBundle xmlns="http://soap.sforce.com/2006/04/metadata">
    <apiVersion>57.0</apiVersion>
    <isExposed>true</isExposed>
    <targets>
        <target>lightning__RecordAction</target>
        <target>lightning__RecordPage</target>
    </targets>
    <targetConfigs>
        <targetConfig targets="lightning__RecordAction">
            <actionType>Action</actionType>
        </targetConfig>
    </targetConfigs>
</LightningComponentBundle>

Output: