Check if User Meta has Existing Value

If I understand correctly, you are wanting to prevent duplicate IDs in the meta data: use the get_user_meta() function to retrieve the meta value and check it for the ID (untested):

$meta = get_user_meta( $user_id, 'saved_session' );

if ( ! in_array( $post_id, $meta ) ) {
    add_user_meta( $user_id, 'saved_session', $post_id );
}

For others that may arrive here:

If the intent is to have only one value in saved_session, then the add_user_meta() function has a fourth parameter $unique that if set to true will prevent meta with an existing key from being updated or added to.

$unique bool Optional Whether the same key should not be added. Default: false

add_user_meta( $user_id, 'saved_session', $post_id, true );