Section 21 of HB 1068, which deals with Article 38.35 Forensic Analysis of Evidence; Admissibility, says that this Article applies only to proceedings commencing on or after the effective date of the act. Is Section 21 actually a part of the statute (law) or would it be considered akin to legislative history?

The effective date is part of the law, as passed by the Legislature. However, it is generally not codified into whatever code reports the new law. One has to reference the legislative act as the authority. For example, see Acts 2003, 78th Leg., ch. __, sec. __.