How do I do a search in File Explorer that includes subfolders of zip archives?

There are a few things that you will need to keep in mind.

First of all, you will want to ensure that the your zip files are indexed properly:

1. Press + S
2. Type Indexing Options and press Enter
3. In the subsequent window click on the Advanced button (and acknowledge UAC, as necessary)
4. Select the File Types tab
5. Scroll down and select the Zip file extension

6. Ensure that zip files are configured to Index Properties and File Contents, as seen below:

   

   (Source)

Next, within the File Explorer interface you will want to select the Search field and confirm that the Search Tools tab is configured within the Location section to search inside All subfolders, as seen below:

Finally, within the File Explorer interface you will want to select the Search field and confirm that the Search Tools tab is configured within the Options section and modify the Advanced options to search inside Zipped (compressed) folders in non-indexed locations, as seen below: