I met a problem I don’t know how to fix it. I chose a way that add custom metadata to filter, if I use that custom metadata as smart group condition, the smart group counter is empty or show slowly,
Not enough information. Please post a screenshot of your smart group and complete screenshots of what you’re seeing elsewhere. Just a tiny number doesn’t provide enough context. Obviously.
No. The white on black stuff is hardly legible at all, then you cram a lot of information into a single image, and the screenshot of the smart rule is not showing the condition.
If you want help, don’t make it unnecessarily difficult for others to provide that help. Redacting out all useful information is pointless.
Every time you visit [a] smart group, DEVONthink runs the attached search and displays it as the content of the group.
The item count of some smart groups can be updated in the background, presumably because they don’t require a full search. Other smart groups, especially those involving text search condition(s), do observe the description as stated in the manual: You need to visit the smart group for it to run the search.