Actually, I’d expect the opposite. If WP Cloudflare Super Page Cache plugin I assume is this one WP Cloudflare Super Page Cache – WordPress plugin | WordPress.org? Don’t really use this plugin but I did evaluate it for my needs in my Centmin Mod LEMP stack’s Wordpress auto installer for my users.
Actually with WP Cloudflare Super Page Cache plugin, it is used to cache dynamic HTML pages using Cloudflare CDN Cache via either CF Page Speed Rules or via CF Worker based caching using CF Cache Everything rule and implement bypass cache on cookie.
If you disable the plugin, I’d expect dynamic HTML pages to return a DYNAMIC status. Now when you enable the plugin, you probably need to configure settings to enable dynamic HTML caching which you haven’t done so? Plugin would of asked for CF API Token or Key for your domain zone so the plugin can setup CF Page Rule or CF Worker for dynamic HTML caching. I suspect that is what happened if it’s that WP Cloudflare Super Page Cache plugin given the response header returned being
x-wp-cf-super-cache-cookies-bypass: swfpc-feature-not-enabled. Which suggests you didn’t enable guest full dynamic HTML page cache with bypass on cookie.
FYI, Cloudflare by default doesn’t cache dynamic HTML unless you use Cache Everything rule, so with plugin disabled it could of removed your CF Page rule? When I did test that plugin, if you disable or remove it, it will auto remove the CF Page Rule or CF Workers it setup for your domain zone - even remove the existing CF Page Rule if it matched the path - so double check if your CF Page Rule is still there.
For plugin support check at [WP Cloudflare Super Page Cache] Support | WordPress.org