In coming weeks, the tops of enormous tower sections for offshore windmills — 300 feet tall and 20 feet around — will rise above the bridge from the harborside, the most visible component of an ambitious, $300 million commitment by the state not only to renewable energy but to Connecticut’s long-ignored maritime economy. After a rocky start, the Connecticut Port Authority is about to complete a redesign and rebuild that has transformed the decrepit Admiral Harold E. Shear State Pier and established it — and by extension New London Harbor — as a principal staging point for construction over the next decade of offshore wind farms on hundreds of thousands of acres of the continental shelf. More importantly, the rebuilt State Pier Terminal, with state-of-the-art infrastructure, heavy lift capacity and access to freight rail, will allow New London — Connecticut’s only natural deep water harbor — to compete into the next century against other East Coast ports for heavy cargo.