The adoption of any charter hereunder or any amendment thereof shall never be construed to destroy any property, action, claims for relief, claims, and demands of any nature or kind whatever vested in the city under and by virtue of any charter theretofore existing or otherwise accruing to the city, but all such claims for relief, claims, or demands vest in and inure to the city and to any persons asserting any such claims against the city as fully and completely as though the said charter or amendment had not been adopted hereunder. The adoption of any charter or amendment hereunder shall never be construed to affect the right of the city to collect by special assessment any special assessment theretofore levied under any law or charter for the purpose of public improvements, nor affect any right of any contract or obligation existing between the city and any person, firm, corporation, or limited liability company for the making of any such improvements and for the purpose of collecting any such special assessments and carrying out of any such contract.