For PageSpeed Insights/Google Lighthouse metrics, TTFB definitely plays apart. But as does optimising your critical render path assets for fast above fold page render. You can have a fast TTFB and still have a slow Google Lighthouse/Insights reported metrics due to your critical render path assets not being optimally configured. Case in point your linked Cloudflare.com PSI results have alot of room for improvement even if TTFB was fast. It’s why Google moved to LCP https://web.dev/lighthouse-largest-contentful-paint as optimising for it involves every step to take in also optimising for FCP and LCP etc - that is your critical render path for above fold loaded assets is key.
If you use Cloudflare paid plans, you get HTTP/2 Enhanced Prioritization support https://blog.cloudflare.com/better-http-2-prioritization-for-a-faster-web/ this is one step up from Cloudflare free plan and allows you to further optimize your visitors perceived above fold render time. It isn’t perfect but in most cases you’ll get a better result than without it. For all other cases you can use Cloudflare workers to fine tune the HTTP/2 priorities via
cf-priority header - in some cases you can tune for better Speedindex, FCP, LCP but at expense of TTI, TBT and full page load.
I suggest you take a read of Performance Tutorials - Google PageSpeed & Webpagetest.org to understand what Google PageSpeed Insights results mean for both real world (field/origin data) and synthetic (lab) data measurements
Recent post in that thread highlights how real world visitors can impact your real world field/origin metrics too.
TTFB is relative to your origin server’s geographical/network distance from the visitor or test server doing the page speed testing. So ideally you want origin server closest to the majority of your visitors.
Basically, if you web host origin server is closer to your visitors and test location, then it will be faster. This is due to Cloudflare not caching HTML content by default (see below). This means your dynamically generated HTML content will be served from origin as it is not cached. So how fast a page is will be determined by your origin web server/php processor speed. So tuning and optimising your origin server will help at web server, php, mysql database server level etc.
So for optimal speed, you want your origin real web server to be hosted in a location closest to your majority traffic visitors and then put Cloudflare in front. For instance, my forums has 50% US visitors 40% Asian visitors and 10% Oceania. So my optimal geographic location for my origin is US West Coast as it sits in middle of US, Europe and Asian so equal round trip times for majority of visitors.
Cloudflare cache certain static content https://support.cloudflare.com/hc/en-us/articles/200172516-Which-file-extensions-does-Cloudflare-cache-for-static-content- but not dynamic/static generated html itself by default. But you can tell Cloudflare to cache dynamic/static generated html content to some extent depending on Cloudflare plan you’re on via cache everything page rule or use Cloudflare Workers with custom cache everything for guest visitors only. But have to be careful to only do this for static html content and not dynamic html content (otherwise you would cache private logged in user content).
I’d test your web site via webpagetest.org as they have alot of geographic test locations and allow you to test real mobile devices and different browser clients and connection speeds and test and reports those additional Google focused pagespeed metrics.
I wrote a guide for my users which maybe useful to you as well on my forums at https://community.centminmod.com/threads/how-to-use-webpagetest-org-for-page-load-speed-testing.13859/
My Wordpress blog using Cloudflare https://developers.google.com/speed/pagespeed/insights/?url=https%3A%2F%2Fservermanager.guide%2F hosted on Upcloud $5/month KVM VPS using my optimised Centmin Mod LEMP stack Wordpress installer in US West Coast region (my fav)