Cars, carts, motorcycles and mopeds are all vehicles and Florida's law rules. 316.003 – Definitions
(77) Street or Highway
(a) The entire width between the boundary lines of every way or place of whatever nature when any part thereof is open to the use of the public for purposes of vehicular traffic;
(b) The entire width between the boundary lines of any privately owned way or place used for vehicular travel by the owner and those having express or implied permission from the owner, but not by other persons, or any limited access road owned or controlled by a special district, whenever, by written agreement entered into under s. 316.006(2)(b) or (3)(b), a county or municipality exercises traffic control jurisdiction over said way or place;
Local authorities may enact ordinances related to golf carts on sidewalks under certain circumstances. That does not seem to include operating golf carts in bike lanes
s. 316.008 – Powers of Local Authorities
(7) A county or municipality may enact an ordinance to permit, control, or regulate the operation of vehicles, golf carts, mopeds, motorized scooters, and electric personal assistive mobility devices on sidewalks or sidewalk areas when such use is permissible under federal law. The ordinance must restrict such vehicles or devices to a maximum speed of 15 miles per hour in such areas.
Other statutes apply to the operation of golf carts in the roadway.
s. 316.212 – Operation of Golf Carts on Certain Roadways
The operation of a golf cart upon the public roads or streets of this state is prohibited except as provided herein:
(1) A golf cart may be operated only upon a county road that has been designated by a county, a municipal street that has been designated by a municipality, or a two-lane county road located within the jurisdiction of a municipality designated by that municipality, for use by golf carts. Prior to making such a designation, the responsible local governmental entity must first determine that golf carts may safely travel on or cross the public road or street, considering factors including the speed, volume, and character of motor vehicle traffic using the road or street. Upon a determination that golf carts may be safely operated on a designated road or street, the responsible governmental entity shall post appropriate signs to indicate that such operation is allowed.
The full statute is here:
Chapter 316 Section 212 - 2016 Florida Statutes - The Florida Senate
s. 316.003 – Definitions
(64) Roadway – That portion of a highway improved, designed, or ordinarily used for vehicular travel, exclusive of the berm or shoulder.
Note that the paved shoulder is not part of the roadway and that vehicles must be driven on the roadway.
s. 316.081– Driving on Right Side of Roadway; Exceptions
(1) Upon all roadways of sufficient width, a vehicle shall be driven upon the right half of the roadway
s. 316.081 – Driving on Right Side of Roadway; Exceptions
(2) Upon all roadways, any vehicle proceeding at less than the normal speed of traffic at the time and place and under the conditions then existing shall be driven in the right-hand lane then available for traffic or as close as practicable to the right-hand curb or edge of the roadway
s. 316.081 Driving on right side of roadway; exceptions
(2) Upon all roadways, any vehicle proceeding at less than the normal speed of traffic at the time and place and under the conditions then existing shall be driven in the right-hand lane then available for traffic or as close as practicable to the right-hand curb or edge of the roadway except when overtaking and passing another vehicle proceeding in the same direction or when preparing for a left turn at an intersection or into a private road or driveway.