Update statements - capture errors and continue with the rest, Sql Server

Language: Layout:

create table dbo.error_handler_log (
        id int identity(1,1) not null primary key
      , error_date datetimeoffset(7) not null
      , severity tinyint not null
      , [state] tinyint not null
      , [number] int not null
      , line int not null
      , [procedure] sysname null
      , message nvarchar(2048) 
    );
    go
    create procedure [dbo].[error_handler_sp] as 
    begin 
      set nocount, xact_abort on;
      declare
          @error_date datetimeoffset(7) = sysdatetimeoffset()
        , @severity tinyint = isnull(error_severity(),16)
        , @state tinyint = isnull(error_state(),1)
        , @number int = isnull(error_number(),0)
        , @line int = isnull(error_line(),0)
        , @procedure sysname = error_procedure()
        , @message nvarchar(2048) = error_message();
      insert into [dbo].[error_handler_log] 
        ([error_date],[procedure],[severity],[state],[number],[line],[message]) values 
        (@error_date, @procedure, @severity, @state, @number, @line, @message);
      --raiserror(@message, @severity, @state);
    end;
    go
        begin try;
      select 1/0 as err;
    end try
    begin catch;
      exec dbo.error_handler_sp;
    end catch;
    begin try;
      select 1/0 as err;
    end try
    begin catch;
      exec dbo.error_handler_sp;
    end catch;
    begin try;
      select 1/1 as one;
    end try
    begin catch;
      exec dbo.error_handler_sp;
    end catch;
    
    select *
    from dbo.error_handler_log;

View schema
Execution time: 0,03 sec, rows selected: 3, rows affected: 0, absolute service time: 0,16 sec