There are several factors which determine how sites with too many ads are dealt with in Google Search.
John Mueller has pointed to several algorithm updates which would impact a site with lots of ads and poor user experience. The page layout algorithm impacts sites with too many ads above the fold. The page speed algorithm impacts pages that are slow, such as those with a large abundance of ads. The core web vitals algorithm, which is launching in May 2021, will specifically impact sites with a suboptimal user experience.
These would all impact the ranking of a site which has too many ads, effectively lowering their rank in search results. However, they are still able to rank highly if they’re particularly relevant to a search query. Sites with a bad user experience are rarely removed from search unless they add zero value. Mueller said that some small businesses have poor sites due to lack of knowledge, and it would be unfair to ban site from Search too easily.