One of the first major shakeups was Google announcing that SSL/https would start being factored into rankings around mid '18 (though it was always a weak signal since around 2010). The last year or so, speed has also increasingly become important with Google's "mobile first indexing", as previously was mostly factored for desktop search.
With that many errors, your server environment is of course important but also consider aspects such as a good caching system, CDN or optimized asset delivery. In your speed tests though, your server performance can be checked with "time to first byte", or TTFB which anything under 200ms is great.
Without knowing details of your site, sometimes even front-end elements such as embedded content, iframes and widgets can cause severe page rendering issues due to calling external scripts etc. Also check your page file sizes, which are much more important on mobile - the higher the page size, the slower the loading/rendering, and thus higher the bounce rate. As bounce rate is also a ranking signal, you can easily get a double whammy here.
Good luck on your server move!
searchengineland.com
, as well as scan with a few other tools.