Update SQL column with SELECT statement data

I am currently working with DB Browser and I have a problem with updating columns. I have a table which contains two columns: one is filled with strings and the other one is completely empty.

I have trimmed these strings with rtrim():

SELECT rtrim(column1, 'e') FROM table1

Now I want to place these trimmed strings into the empty column:

UPDATE table1 SET column2 = (SELECT rtrim(column1, 'e') FROM table1)

But now it fills the empty column with only the first trimmed string of column1, because it won't see the SELECT statement as a column, but as a string. I also tried:

INSERT INTO table1 (column2) SELECT rtrim(column1, 'e') FROM table1

But this just doubles the amount of rows, as column2 is not 'empty', but filled with null.

I want to get something like

| column1 | column2 |
---------------------
|  apple  |  appl   |
|  orange |  orang  |
|  grape  |  grap   |

Any ideas on how to solve this?