I am using Yandex Metrika for my site Thegoldlive.com and facing a Core Web Vitals issue due to it. I believe it's the main reason due to why my site is getting slow. Any way to get rid of it or should I remove this from the site?
When I remove it from the site, the speed of my site gets better. But, I don't want to remove it because it helps me analyze the visitors on site in the best manner. So that's why asking, is there any way to keep both things parallel?
Running your site through PageSpeed Insights it appears your issues are with loading time (TTFB, FCP, and LCP) and shifting content (CLS).
I'm not familiar with Yandex Metrika, but it seems unlikely an analytics solution will slow down these metrics. Mostly they affect responsiveness metrics like FID and INP.
I can't quite see the reason for slow TTFBs (it seems fast to me!), which will directly affect the other loading metrics. You seem to be using a CDN (cloudflare) and the server response time from lab tests seems fast.
It could be you just get a lot of visitors from slow networks/devices? If so one thing that can help here is ensuring sites are eligible for the Back/Forward cache, so at least they get a fast (instant!) load when going back and forwards within the site. Testing your site for this shows your site is using an unload handler, meaning you can't benefit from this performance gain. It looks like you are using Cloudflare's Rocker Loader - ironically something that's supposed to improve performance but that might be holding you back here. I'd turn that off.
For your layout shift issues (CLS), it's must more obvious. You have an advertisement that pops in and out and pushes all the content down. You'd be better to reserve a block of white space for that to slot into, rather than have it dynamically inserted and moving the text around, which is an irritating experience for site visitors.