SQL Server Task Wizard – How to Specify Import Row Range

At the end of the import/export wizard you have the option to save your SSIS package (yes that's what the wizard uses behind the scenes). Save your package to a file then open it in SQL Server Data Tools. Go into the data flow and open the source. In the "Error Output" tab you will see an option to ignore failure (for truncation specifically or errors in general). Modify it for the columns you are worried about.

All that being said you are probably(99.999%) not seeing a truncation because the column is to big to fit in a varchar(max). What is probably happening is that SSIS "thinks" your column is shorter than it is. If you go into the connection manager for your CSV file you can modify the "width" of your input columns in the advanced tab.

The method of insert doesn't appear to be the problem, more the data itself

The error you are receiving is because one of the columns you have in your database table is too short (see your column 'wikipedia_link') see what length it is and if you can increase it, note it is quite possible to have more errors on other columns that are similar, judging by the data contained in that field the longest field is 128 characters, so I'd make the field nvarchar(130) as a minimum

If you load the csv in excel you can find out the max length of a column by using {=MAX(LEN(Q:Q))} (NOTE to get the {} array calculation after typing the query press ctrl + shift + enter)

Check all your fields are long enough and try again