get_query_var( 'tag' )
will return you 'tag1+tag2+tag3'
string.
get_query_var( 'tag_slug__and' )
will return you the array of tags.
So, there are two ways to achieve the goal:
$args = array(
'tag' => get_query_var( 'tag' ), // string
);
or
$args = array(
'tag__and' => get_query_var( 'tag_slug__and' ), // array
);
It remains to be seen how do you plan to create tag1+tag2+tag3
slug.