In general, electric bicycles are considered "bicycles", rather than motor vehicles, for purposes of the code. This implies that all bicycle regulations apply to electric bicycles including operation in bike lanes. Exceptions to this include a restriction of operation on sidewalks and that a license or permit is required if the rider is younger than 17 years of age.
DIY Kit ebikes – Ebikes that are home built with a DIY kit, and exceed the 750W/20mph definition, are also allowed to be bought, build, and ridden. DIY kits are throttle activated. Some of the newer systems have PAS options. Ebike kits are not unilaterally prohibited or assigned motor vehicle status, but again, legal classification and road use falls under state law.
How do the State Laws relate to the 2001 Federal Law? This is a difficult question to answer and know how they apply to you individually. From the Federal Law, one would hope that your purchased ebike is simply classified as a bicycle, with all the rights and privileges allotted to a normal cyclist. However, State Laws are confusing because they may be more restrictive in parts and add other requirements. About 30 U.S. states still have confusing regulations around them. Either the bikes are technically classified as mopeds or motor vehicles, or they have equipment, licensing or registration requirements that cause problems for riders. Thanks to the People-For-Bikes/Bicycle Product Suppliers Association (BPSA) partnership with local advocacy groups, they have been able to make the case for streamlining state regulations so that e-bikes are essentially treated like regular bicycles.4
On the other hand, the battery doesn’t lock into the bike, which means you can’t just leave it on your bike when you park at the bike rack. Anyone could walk by and simply remove your battery. That seems like an oversight to me, though perhaps the designers assumed that such a small battery would just be easy to take with you. And it is. My wife could probably lose this battery in her purse.