Hello Peter,
From the additional screenshot shared, it seems you are creating Multiple lines of text columns in the SharePoint Online list. So, when I check the behavior at my end, I also have the same result as your end. Based on my further finding, a SharePoint Multiple lines of text column can store up to 63,999 characters and I also tested with more than 5000 characters, I can save the list item without any problem.
So, you no need to enable any option to save more than 255 characters in Multiple lines of the text column.
Best Regards,
Chitrahaas