Google Analytics & Booking Engine

Hi, My name is Junior, i manage a small hotel in London and have recently set up a new website with wix - https://www.athenahotellondon.co.uk/. I hope i can get some assistance, We are a hotel and we use wix for our homepage for our website. We us book now buttons on our site to redirect guest to our booking engine which is with cloudbeds.com, https://hotels.cloudbeds.com/en/reservation/lpQ4HO/?currency=gbp. I have set up google analytics but i have no idea if it is tracking correct the data, i also set up google tag manager to get the third cookies from the booking engine, but again i don't think its set up correctly. I need help to make sure everything is set up correctly so i can see the full customer journey and also in google analytics help to find out the data i need once everything is set up. Additionally i heard google are stopping third party cookies so once this stops how would i go about tracking the process.