All vested rights of the city shall continue to be vested and shall not in any manner be affected by the adoption of this Charter; nor shall any right or liability, or pending suit or prosecution, either in behalf of or against the city, be in any manner affected by the adoption of this Charter, unless otherwise herein expressly provided to the contrary. All contracts entered into by the city or for its benefit prior to the taking effect of this Charter shall continue in full force and effect. All public work begun prior to the taking effect of this Charter shall be continued and perfected hereunder. Public improvements for which legislative steps shall have been taken under laws in force at the time this Charter takes effect may be carried to completion in accordance with the provisions of such laws.