There are no height restrictions along Congress related to the Capitol View Corridor (CVC) except for banning any skywalks/skybridges from crossing the street. There are height restrictions related to the CVC on the surrounding streets, however, north of 10th Street.
This link has some historical information about height restrictions in Austin related to the Capitol.
http://www.heritagesocietyaustin.org/CVCBackground.pdf
Capitol View Corridor map.
http://www.ci.austin.tx.us/downtown/...port_Final.pdf