how to modify the size of a column

Regardless of what error Oracle SQL Developer may indicate in the syntax highlighting, actually running your alter statement exactly the way you originally had it works perfectly:

ALTER TABLE TEST_PROJECT2 MODIFY proj_name VARCHAR2(300);

You only need to add parenthesis if you need to alter more than one column at once, such as:

ALTER TABLE TEST_PROJECT2 MODIFY (proj_name VARCHAR2(400), proj_desc VARCHAR2(400));