Step one - determine (or tell us) if these are all one circuit (and are there garage lights other than the opener and your bench lights, and are those on the same circuit as any/all the outlets, or not?)
Step two - there are rules of thumb, though they can be adapted to actual use-cases, such as your low-draw LED lights. Following them won't keep things happy if too many heavy-duty things are all running at once. Exceeding them won't make the circuit blow if 27 outlets each have a 10 watt LED light plugged in. 8 (duplex) receptacles on a 15 amp and 10 on a 20 amp circuit is one such RoT - I've also seen 7 suggested. As such your plan to add 4 duplex would fit within nearly every RoT on a 20 amp circuit with 3 outlets now. Also, you are running the same stuff now on the same circuit without trouble, which is a good sign, until you add more stuff running at the same time, or open the garage door while running a power saw and sprinkling the lawn.
If you have a panel/sub-panel in the garage, running a new circuit is probably worthwhile - if it needs to come from the house main panel, that may be more work and expense than you want to go to for a setup that works now from extension cords.
The wires for your outlets would run from the LOAD side of the GFCI (there may already be wires connected there if it's all one circuit in the garage) and then run to the first outlet, from the first to the second, etc.
Generally this is made of "Nope".
You hope to use flexible cordage.
Cordage needs to be correct for the task. A random extension cord won't cut it - believe me, I've struggled a lot to find longer cords I can put on 4' fluorescent fixtures. (I don't want to splice plugs on them, I want premade plugs).
Cordage needs to have proper grommeting/strain relief anytime it enters or exits a listed electrical box.
You can't attach cordage to walls. You might be able to run it through surface mount conduit.
You definitely can't route cordage through a doorway, whether there's a door or not.
Other than that, Mrs. Lincoln, use of cordage is not strictly prohibited. It's fine for the short jumper between a lamp properly physically mounted, and a nearby outlet which has been installed for that purpose. In fact, look "up" in a CostCo ceiling and you'll see a lot of that.
Maybe you should ask your landlord to install just that.
Speaking of that... The lamp needs to be properly hung from the ceiling. "any old way" won't do, it must be hung by a UL listed method. That is because if the lamp falls down, it will tear out its cordage, which will start a house fire or electrocute someone.
The home was provisioned to you with switched outlets along the floor. The purpose for those outlets is to plug in floor lamps. That is the right way to light the room.
If you like ceiling light... remember the terrible old halogen torchiere lights which stood 6' tall and had a 500W halogen bulb lighting the ceiling (which started fires)? Those were brought to market for this very problem. The good news is, today, you should be able to find modern LED versions that are maybe 30-50 watts.
Unless you investigate house fires for a living, you can't go with your own intuition of "safe". People who do... have written a big book. It's called the National Electrical Code.
The book is the reference standard used by insurance agents, prosecutors and judges. When a tenant violates Code, he creates a very ugly liability situation because the home insurer won't pay the landlord for the fire loss, leaving him to go after you. After you deal with the criminal justice system, you file bankruptcy to shake off the civil debt, and get a big surprise.
As a landlord I might be mellow about an alteration that was to code. But if not, I'd call the building inspector in, and he'd condemn the house and you'd be out. This method overrides rent control, 30 day notices and the like.
Best Answer
Extension cords are not supposed to be used for permanent fixtures. These fixtures are supposed to be hard wired or directly plugged into a permanent outlet.
A common approach to solve this problem would be to install a switched outlet on the ceiling near the fluorescent lights. In many jurisdictions, you could use non-metallic cable to run the outlet and the switch. In some, you might have to either snake the cables in the wall or use surface raceways.
You could ask your landlord to make this change. Good luck.
Reducing the number of extension connections would somewhat improve safety, and ensuring that cords are not dangling in walking space or prone to being pulled or tripped over would reduce risk. One extension cord to the fixture is better than a cord and a power strip. Also make sure that any extension cord is three wire. DO NOT BYPASS THE GROUND PIN! But any of these patches are less than what is considered safe practice.
At very least, you may want to install a GFCI outlet wherever the cords are ultimately plugged in. This would provide some protection in the event of failure of the fixture or the cords.