while I have a number of issues with smart search and the old search is not working on my upgraded site...
I have made a clean install of J4.1 to test the smart search / finder operation.

smart search includes _archived_ content by default.

filters were unable to remove archived pages

on my clean install I added a page called...

• published art which was published
• unpublished art which was unpublished
• archived art which was archived
• trashed art which was trashed

and did a search for art - finder displays ...

• published art
• archived art

I don't want archived pages showing up in my search results...
to stop this "feature" from happening...
open administrator\components\com_finder\src\Indexer\Adapter.php
navigate to the bottom of the page - (line 901 on my file) and look for "case 2: " then comment it out like this...

// Published ~and archived items only~ should return a published state
case 1:
// case 2:
return 1;

go to administrator panel > components > smart search > index and press the "index" button at the top

search should omit them from search results. (Your mileage may vary - you may need to delete the index and do a re-index)

Be aware - future updates may break these changes, so until they are included in the core, you may need to redo this process every time you update Joomla.

Hope it helps someone.

(explanation...
case -2 is trashed
case 0 is unpublished
case 1 is published
case 2 is archived)

Originally posted by @nzyeehaa in #37754 (comment)