On occasion, my Backdrop website will go down. When you visit the site, you get the following error message: "SQLSTATE[08004] [1040] Too many connections." It's intermittent and usually goes away within a few minutes. But it's been happening more frequently since the last Backdrop update. That could just be a coincidence, but I wanted to see if anyone has suggestions about what's going on.

At least at first glance, this appears to be a hosting issue. I have two other websites on the same shared hosting plan, both built in WordPress, and when the Backdrop site goes down, the WordPress sites go down as well, with a different message ("Error establishing a database connection.")

But the WordPress sites are tiny, just a few pages each, whereas the Backdrop site is massive, with thousands of pages.
I've gone round and round with my hosting provider. Here are some of their suggestions:
"Too many connections is typically a temporary issue that can occur when your website experiences a peak in resource usage."
"If the issue persists, we strongly recommend reducing factors that may contribute to excessive connections, such as limiting the number of cron jobs and disabling any unnecessary plugins."
"Currently, your websites are loading correctly, and their current resource usage is within normal limits. The SQLSTATE[08004] [1040] Too many connections error typically means the database hit its connection limit. However, we did not find any significant traffic spikes or server issues during the reported time."
"Given that this is an intermittent issue, it may be caused by bots or crawlers overloading the server." (In response to their suggestions, I modified robots.txt to ban a list of AI crawlers and increased crawl delay from 10 to 30 seconds. But the problem persisted.)
Though I'm on a shared hosting plan, it's the highest-performing and (and costliest) plan offered by my provider, Hosting.com (formerly A2 Hosting). I use a free Cloudflare plan for content delivery on the Backdrop site, but not the WordPress sites. This has been happening intermittently since I relaunched the main site in Backdrop, but it's gotten worse in the past week.
Also, when we had some problems with the Backdrop sites, this is what the server admin did: