Select truncated string from Postgres

The n in varchar(n) is the number of characters, not bytes. The manual:

SQL defines two primary character types: character varying(n) and
character(n), where n is a positive integer. Both of these types can
store strings up to n characters (not bytes) in length.

Bold emphasis mine.

Use left() to “truncate” a string to a given number of characters:

SELECT left(my_val, 4095);

Or cast:

SELECT my_val::varchar(4095);

The manual once more:

If one explicitly casts a value to character varying(n) or
character(n), then an over-length value will be truncated to n
characters without raising an error. (This too is required by the SQL standard.)

The former returns text and is typically preferable – unless you expressly need the type varchar(4095). The result will be coerced to text in most contexts anyway.