When you move your web site from one host to another, Google generally knows about it. When Google detects the change, it can and likely does attempt to relearn how fast and frequent it should crawl your site. Gary Illyes from Google said this on Twitter this morning.
He said "Fun fact: changing a site's underlaying infrastructure like servers, IPs, you name it, can change how fast and often Googlebot crawls from said site. That's because it actually detects that something changed which prompts it to relearn how fast and often it can crawl."
Here is the tweet along with his #cattax hashtag:
.Fun fact: changing a site's underlaying infrastructure like servers, IPs, you name it, can change how fast and often Googlebot crawls from said site. That's because it actually detects that something changed which prompts it to relearn how fast and often it can crawl.#cattax pic.twitter.com/1meuxbdbKi
— Gary 鯨理/경리 Illyes (@methode) November 23, 2020
Gary did say that CDNs are special in this regard:
CDNs are generally special-cased on our side because they're... well... special
— Gary 鯨理/경리 Illyes (@methode) November 23, 2020
Will changing servers but leaving everything else the same impact rankings? It really should not unless Google cannot crawl your site due to server issues.
Forum discussion at Twitter.