What else should be done if I went to my sites dir in Linux and ran this command:
sudo wp search-replace 'http://' 'https://' --all-tables && wp cache flush
and still, some images are loaded as http and not https.
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In this site I use Elementor. I solved it by going to WP-admin > Elementor > Tools > Change address, and there I've changed all http:// to https:// as well.
Then the problem solved.
I admit I have no idea why the WPCLI search and replace operation didn't cover Elementor tables as well.