Elementor Library: Not connected (cURL error 28: Connection timed out ...)

When I had the same issue it helped to disconnect my elementor account and therefor its licence. Reactivating also reactivated the connection to the template library which seems to be handled seperately from the rest of the elementor plugin.

Using Elementor 2.1.4, I was not able to resolve this issue by reinstalling the plugin, reactivate the license, disabling other plugins, using the 'Sync Library' tool.

What worked for me was replacing

  s:10:"categories";N;

with

  s:10:"categories";a:0:{}

in the option_value field of the entry in the wp_otions table in the database where

 option_name = 'elementor_remote_info_library'

This value gets updated from time to time, so to avoid the categories getting set to null again you might also want to commment out the following line in wp-content/plugins/elementor/includes/api.php@111 right before the update_option( self::LIBRARY_OPTION_KEY, ...):

    $info_data['library']['categories'] = json_decode( $info_data['library']['categories'] );

which causes this issue, as the categories already are available as array instead of JSON at this point.