I wrote this procedure (q2). When I run q1, I get the error :

Msg 11529, Level 16, State 1, Procedure sp_describe_first_result_set, Line 1
The metadata could not be determined because every code path results in an error; see previous errors for some of these.
Msg 2812, Level 16, State 62, Procedure sp_describe_first_result_set, Line 1
Could not find stored procedure 'master.dbo.usp_checkLinkedServer'.

q1:
DECLARE @StatementToRun VARCHAR(MAX)
SELECT @StatementToRun = StatementToRun FROM OPENQUERY("linkedserver", 'EXEC master.dbo.usp_checkLinkedServer')
SELECT @StatementToRun
EXEC (@StatementToRun)

q2:
create PROCEDURE usp_checkLinkedServer (
@sysservername varchar(1000) = 'server'
)
AS
set nocount on
  DECLARE @LinkedServerDBCheck NVARCHAR(2000)
    Declare @count int;
    --Print 1
      BEGIN TRY
   IF EXISTS(SELECT * FROM sys.servers WHERE name = @sysservername)
        BEGIN
        --SELECT @sys= CONVERT(sysname, @sysservername);
   -- EXEC @retval = msdb.sys.sp_testlinkedserver @servername = @sysservername;
   --SELECT 1;
        SET @LinkedServerDBCheck = 'SELECT 1 FROM '+@sysservername+'.master.sys.databases WHERE name = ''master'''
        --select @LinkedServerDBCheck
   EXEC sys.sp_executesql @LinkedServerDBCheck
   SELECT @Count = @@ROWCOUNT

        IF (@Count > 0)
        BEGIN
          print 'LINKED SERVER ''' + ISNULL(@sysservername,'') + ''' Works.'
        END
        ELSE
          PRINT 'LINKED SERVER '''+ ISNULL(@sysservername,'') + ''' DOES NOT Work!'
END
    
  END TRY
  BEGIN CATCH
   SELECT 0;

  END Catch