Postgres won’t accept table alias before column name

The problem is that you include the table alias in SET clause, in the columns. See the documentation of UPDATE in Postgres docs:

column

The name of a column in table. The column name can be qualified with a subfield name or array subscript, if needed. Do not include the table’s name in the specification of a target column — for example, UPDATE tab SET tab.col = 1 is invalid.

This is valid in Postgres:

update GREETING Greeting 
set 
    NAME='World', 
    PHRASE='Hello World!' 
where Greeting.ID=5 ;