Cloudflare Web Analytics is just the JavaScript Beacon Analytics. It doesn’t have any plan specific features, no such thing as “Pro Analytics”, and how would it have data before you installed the js code?
Cloudflare does have Website/Zone Analytics, server-side analytics on proxied traffic. Pro would give you more features with that, “Web Traffic Analytics”, but your website isn’t proxied through Cloudflare, and those are seperate from Web Analytics/the JS Script.