A saved search is created as a subfolder under the parent folder that was set when the saved search was created, e.g. it could be a subfolder of Inbox. If you want to apply the saved search, right-click the saved search folder, Properties, change the search filters, then click Update.

http://kb.mozillazine.org/Saved_Search

Just to get a better idea of what these search folders look like and how to distinguish them regular email folders, I created a second search folder and this time included the word search in the folder name. Then I could see the new search folder plus the original one (which was named poorly). Just to make sure, it looks like the search folders have the regular folder icon, but they also have a magnifying glass (common windows search icon) inside the folder icon (at least on my system). There is another Thunderbird Help item that has a picture of the primary Thunderbird window showing the email folders, and in that picture the search folders look different in that they are pink and don't appear to have the magnifying glass icon. Is that difference due to the fact that I am running a fairly old version (78.14)? I tend to have a "if it aint broke don't fix it" policy, so I don't update software unless there's a problem or a new feature I want.

I'm only familiar with the display with the magnifier on the folder icon. Perhaps you can post a screenshot of the pink folders, or explain how to show them. But I don't think the function of saved searches has changed in recent years and TB versions.

I don't know how to do a screen shot but here's a link to the Thunderbird help article I mentioned. It includes the image of the folder screen I mentioned.

https://support.mozilla.org/en-US/kb/using-saved-searches

The saved search folder in the article was created as a subfolder of the account, which is why it isn't indented like a subfolder of an account folder, e.g. if it was created as a subfolder of Inbox. Other than that, there's no difference in the usage.