Does your hosting provider affect SEO?
The short answer
Indirectly, yes. Google rewards fast, stable websites, and your hosting determines part of the load time and uptime. A slow or frequently unreachable host costs you positions. Between good providers the SEO difference is small. Optimizing your site itself matters more.
In detail
Google uses site speed and user experience (the Core Web Vitals) as ranking factors. The server is the first link in that chain. How fast it responds matters before your site even starts loading. Slow budget servers and overcrowded shared hosting show up there. Modern providers with NVMe storage and good caching do fine.
Server location plays a minor role. A server near your audience responds faster. For a US audience, hosting in the US makes sense, and a CDN largely evens out the rest. More interesting is consistency. A host that slows down every day at peak time drags your metrics down invisibly.
More important than choosing between two good hosts is what you do yourself, with optimized images, caching, a light theme, and restraint with plugins. A well-built site on a mid-tier host beats a sluggish site on premium hosting every time. Pick a solid provider, then put your energy into the site.