Many beers are filtered to remove the yeast since it's not really desirable once fermentation has completed. BUT - and a big "but" - there are styles like hefeweizen and other unfiltered beers that deliberately leave the yeast in for flavour.
Beers are also sometimes fermented with organisms other than Saccharomyces. These organisms contribute a wide variety of flavors, generally funky or sour.
Many beers are unfiltered because the filtering process can remove other, desirable flavors (mostly hops). Filtering used to be very rare in American craft beer for this reason.
Hefe literraly means yeast in German.
So a Hefeweizen translated literally would be a "yeast wheat".
Very tasty beer though. And I have the same issue. Still my favorite beer: Erdinger Weizen. Preferably the dark one. But it has a ton of yeast on the bottom. And I get gastro issues very quickly when I start drinking them again. Non alcoholic versions don't help.
I've discovered that Schneider Weisse 0.5% and, to some degree, Rothaus Hefe Weizen 0.5% are less likely to provoke gastro issues while closely mirroring the taste of their alcoholic equivalents.
If you like lagers and don't drink alcohol, I've found those from Fee Damm (Estrella)[1] and Luckysaint[2] to not cause any issues either, particularly the 'Tostada Amber' from Free Damm and the larger from Luckysaint (Their Hazy IPA is great too!).
[1] https://www.damm.com/en/beers [2] https://luckysaint.co/