Currently the count that is shown next to the Error Index submenu entry in the AMP admin menu is uncached and computed dynamically on every single admin page request (that includes the admin menu, so AJAX requests should not be affected).
Strangely enough, the count directly above it for the Validated URLs entry is already being cached.

We should add caching for the Error Index cache as well, and combine these into a single transient.
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We should also add caching for the At a Glance widget while we're at it.
A support topic was just raised about this as well:
Hello
in /wp-admin/admin.php?page=amp-options
I find this:
and for example in my custom plugin, all these unnecessary queries are made on the administration page
May be the same issue or an area for additional query reductions to be made.
Two more related/similar support topics:
Related: #5336.
QA passed
The values are stored in the transients and reused for both the menu construction as well as the "At a glance" widget.

Most helpful comment
A support topic was just raised about this as well:
May be the same issue or an area for additional query reductions to be made.