How can I verify that my SQL Server edition is Express?
You have to check the SERVERPROPERTY ('Edition') AS ServerEdition to find if your installed instance is an Express edition or standard or enterprise.

You can use below T-SQL :

SELECT
   SERVERPROPERTY ('MachineName') AS PhysicalMachineName,
   SERVERPROPERTY ('ServerName') AS SQLServerName,
   SERVERPROPERTY ('Edition') AS ServerEdition,
   CAST(SUBSTRING(@@Version,charindex('SQL',@@version, 1),15) AS VARCHAR(255)) +  ' + ' 
       + CAST (SERVERPROPERTY ('productlevel')AS VARCHAR (50)) + ' + (Build'
       + CAST (SERVERPROPERTY ('ProductVersion') AS VARCHAR (50)) +')' AS ProductVersion


Another variation that tells you the database size limit based on the version (note that -1 means unlimited)

SELECT
   SERVERPROPERTY ('MachineName') AS PhysicalMachineName,
   SERVERPROPERTY ('ServerName') AS SQLServerName,
   SERVERPROPERTY ('Edition') AS ServerEdition,
   CAST(SUBSTRING(@@Version,charindex('SQL',@@version, 1),15) AS VARCHAR(255)) +  ' + ' 
       + CAST (SERVERPROPERTY ('productlevel')AS VARCHAR (50)) + ' + (Build '
       + CAST (SERVERPROPERTY ('ProductVersion') AS VARCHAR (50)) +')' AS ProductVersion
    , case  when cast(SERVERPROPERTY ('Edition') as varchar(255)) like '%express%'
                then 
                    case 
                        when (
                                CAST(PARSENAME(CAST(SERVERPROPERTY('ProductVersion') as varchar(128)), 4) as int) &gt;=10  -- major
                             and CAST(PARSENAME(CAST(SERVERPROPERTY('ProductVersion') as varchar(128)), 3) as int) in (0,50) -- minor
                              ) then 10  -- this is sql server 2008R2 and up
                        when (
                                CAST(PARSENAME(CAST(SERVERPROPERTY('ProductVersion') as varchar(128)), 4) as int) &lt;= 10
                             and CAST(PARSENAME(CAST(SERVERPROPERTY('ProductVersion') as varchar(128)), 3) as int) &lt; 50
                              ) then 4  -- this is sql server 2008 and less
                      end
                        else -1
        end  as EditionLimit


Starting sql server 2008R2, Express edition database limit was increased from 4GB to 10GB.