One specific Florida statute, 316.605 covers this matter directly:
...and all letters, numerals, printing, writing, the registration
decal, and the alphanumeric designation shall be clear and distinct
and free from defacement, mutilation, grease, and other obscuring
matter, so that they will be plainly visible and legible at all times
100 feet from the rear or front.
Italics mine.
A Jacksonville, FL lawyer's blog references a drug case in which the driver was pulled over because the frame around the plate partially obscured the legends at the top and bottom of the plate, typically a state slogan and/or county or other "insignificant" information. Irrespective to this question, the traffic stop was rejected, as the officer was able to read that information as well as the identification information contained in the tag number. The linked article goes on to suggest that one might get away with it if only the legends are obscured, but it appears that the lawyer's opinion also depends on the judge.
In the case of the supplied photo above, it's quite obscured and would create a citing offense if an officer arose from the wrong side of the sleeping furniture.
Other states might be determined by searching [state name] obscured license plate.
User65535 (a rather large binary-1 number) has presented an answer that I see as an omission on my part. Your primary question is how to get around the obscuration of the tag.
You have a number of disadvantages. No trailer hitch means the bike rack is less than solidly mounted, and would not provide a suitable attachment point for a remote tag mount. No trailer hitch means no trailer wiring, which would have been used for a tag light and possibly remote brake lights and turn signal lights, although it's debatable if yours are truly obscured.
Aiming at only relocating the tag, you'd still have to have the ability to illuminate the plate, which mean you'll tap into that wiring lead in some manner.
The answer may be magnets. Magnets with a light and bracket to hold the tag. You'd want to pull the tag and lock it in the trunk when you are away from the vehicle, as creating a convenient magnet mount means convenience for someone to walk by and snap it free of the mount. I'd bet that the lower part of the car is plastic, but the lower right corner of the trunk lid may support magnets.
Additionally, one could consider a strap-through mount. The plate frame (with lights) would be mounted on sturdy fabric straps with parachute clips that lock inside the trunk and wrap around the appropriate portions of the trunk, placing the tag in a visible location, again perhaps the lower right corner.
