When it comes to crawl budget and Google not crawling your site too much or too little, Google takes into account all Googlebot activity across all verticals. So that includes crawling for web search, Merchant Center, ads, and all the various crawling activities.
Google's John Mueller was asked by Christian Radny, "Does merchant center crawling (automatic updates) count for crawling budget?"
John Mueller replied, "Sure - it's a load on your server. The goal is to avoid breaking your server through a high load."
Here are those posts:
Sure - it's a load on your server. The goal is to avoid breaking your server through a high load.
— John 🧀 ... 🧀 (@JohnMu) April 11, 2024
Google has a pretty detailed document on crawl budget over here if you want to dig in more on this topic.
But yes, Google takes into account all crawling activity when it comes to seeing how much Googlebot can crawl your site.
Forum discussion at X.
Note: This was pre-written and scheduled to be posted today, I am currently offline for Passover.
