In short - it does, to some extent. But not THAT much. You shouldn’t really worry about it.
The most important bits to consider for SEO when choosing a hosting provider is:
Server location and domain extension. Choose a server location closest to your target audience’s location. If targeting Canadians, get a .ca domain extension.
Speed. Website loading speed does affect SEO. The faster your website is, the better. So get faster web hosting with SSD, caching, latest software, cloud hosting instead of shared hosting etc.
HTTPS. You should install an SSL certificate, most hosting providers offer a free SSL through their control panel. So you can install it with a couple of clicks. Websites with SSL get better rankings.
Uptime. If your website is down and offline constantly, you’ll of course lose rankings. You may even be deindexed.
Other websites on the same IP. If you’re using shared hosting, you are sharing the same IP address with many other websites. So if most of those websites are spammy, your website will also be associated with “bad SEO”. You can avoid this by getting hosting with a dedicated IP address for your website only.