Congratulations on the improvements you have already made to the speed of the desktop site!
Looking at the WebPageTest report you shared, the Web Vitals section of report is going to be the closest match to what you see in Think With Google.
Regarding your question about Time to First Byte, that metric is often used to help understand how long the initial HTML page takes to process on the server and start arriving at the users browser. It looks like the Time to First Byte for this site is around 800ms. There is room for improvement (a good target is usually below 200ms,) but for this site there may be other items to address first that would likely take less effort to address than optimizing the WordPress server.
Here is a link to a WebPageTest screen where that screenshot was captured:
Lighthouse has specific recommendations that should be helpful in deciding where to focus your efforts. Here is a screenshot of the recommendations for this site:
I would recommend running both Lighthouse and WebPageTest. Lighthouse provides a prescription of what to do, and WebPageTest gives lots of helpful reports and detail.
When running WebPageTest, consider selecting the “Emulate Mobile Browser” and select Motorola G (gen4) which matches what is used in Lighthouse.
Over time, if you find that you cannot get similar device emulation with your current service providers, you may also consider a performance monitoring service that specifically supports mobile emulation.
Good luck with your optimizations!