demo, Sql Server - rextester

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CREATE TABLE [dbo].[Test_Run](
    [ID] [int] IDENTITY(1,1) NOT NULL,
    [Name] [nvarchar](250) NULL,
    [Script] [nvarchar](max) NULL,
    [Last_Result] [nvarchar](100) NULL,
    [Last_Runtime] [datetime] NULL
CONSTRAINT [PK_ID] PRIMARY KEY CLUSTERED 
(
    [ID] ASC
)WITH (PAD_INDEX = OFF, STATISTICS_NORECOMPUTE = OFF, IGNORE_DUP_KEY = OFF, ALLOW_ROW_LOCKS = ON, ALLOW_PAGE_LOCKS = ON) ON [PRIMARY]
) ON [PRIMARY] TEXTIMAGE_ON [PRIMARY]

insert dbo.Test_Run (Name, Script) values ('1st statement', 'SELECT 1');
insert dbo.Test_Run (Name, Script) values ('2nd statement', 'SELECT 2');
insert dbo.Test_Run (Name, Script) values ('3rd statement', 'SELECT cast(getdate() as varchar)');

select * from dbo.Test_Run

declare 
    @id int, 
    @sql nvarchar(max), 
    @last_result nvarchar(100), 
    @last_runtime datetime,
    @params nvarchar(max);

SET @params = N'@retvalOUT varchar(max) OUTPUT';

select @id = min(id) from Test_Run;
while @id is not null
begin
    select @sql = Script from Test_Run where id = @id;
    set @sql = 'select @retvalOUT= (' + @sql + ')';
    exec sp_executesql @sql, @params, @retvalOUT = @last_result OUTPUT;
    set @last_runtime = getdate();
    
    update Test_Run set Last_Result = @last_result, Last_Runtime = @last_runtime where id = @id;
    
    select @id = min(id) from Test_Run where id > @id;
end

select * from test_run

View schema
Execution time: 0,03 sec, rows selected: 23, rows affected: 6, absolute service time: 0,17 sec