Should I use WP speed optimization plugins if I already have Cloudflare?

Yes. Always.

I hate all these naysayers that proclaim more plugins = slower wordpress.

Not so with speed optimization plugins most of the time, as long as their purpose is to do different things. Never have like 4 caching plugins on the same site.

You could try throwing on Autoptimize and fine tuning it to handle the critical CSS more efficiently.

If your server is LiteSpeed compatible, the LiteSpeed cache has tons of options to make things fly, in conjunction with CloudFlare.

If not, the premium version of Total Cache has a ton of options.

Generally, there are four things you want to do from here:
REDUCE THE FILE SIZE OF YOUR IMAGES.
Compress the biggest down manually, maybe with [https://birme.net/](https://birme.net/), and save to webp.
Otherwise, find something that converts all the images to webp.

The other biggest factor is that ‘Eliminate Render Blocking Resources’.
You want something that defers most of your javascript and css, without breaking your site.
I’ve had some success with the LiteSpeed free plugin, on LiteSpeed servers.
Otherwise, Total Cache Premium has an async option as a premium feature.

You could try to mess with the plugin Async Javascript, but that plugin has always been an absolute nightmare to work with for me. As has PhastPress.

Third.

You want something to lazy load images.
Total Cache can do this too, but I typically use WP Rocket’s free plugin.

Fourth.

If you’re running Woocommerce, you need Object Caching and Database Caching.
A lot of hosts out there come with Redis. If yours doesn’t…….
Consider finding different hosting…

There are so many other things . . . .

Nice mess you have: https://yellowlab.tools/result/gtkm5b4vwg

Google fonts, calls to extern form script, anime.js script, slider and 10-15+K DOM elements. Fix these issues before you reach for caching plugins.

Unwise use of cache plugin (defer js) can even break your site. I would start with simplest of all: WPSuperCache or Autopimize. And see does your host provide redis or memcache.