just make the hole smaller. There is 2 way.

easy and purely visual: you can make the hole smaller by screwing strong wire mesh or paste a thick sticker board as the foundation and applied plaster over it.

pro and correct way: use plywood as the foundation, screw the cutout to the plasterboard and apply wet plaster over it. Just buy plywood with screwable thickness and with enough rigid. Cut a square that is bigger than the current hole but once cut half can slip over the current hole (between 8 inch to 11inch for your case). Cut any hole size that you want in the middle of the square board, cut the board in half so you can slip it to the top of the ceiling board. screw it and plaster and sand.

it is the same way how workers seal plaster ceiling holes.


Edit
Mybad, there is 3rd way. Just seal the current hole and switch to external light as these so you wont have similar problem in future.

https://shopee.com.my/24W-LED-Light-Surface...KRoCZTEQAvD_BwE


I recommend the 3rd way. LED light (the driver) kaput more often compare to fluorescent. Worst is the maker very often suka-suka change sizing and spec compare to fluorescent and older light spec.

This post has been edited by chamelion: Oct 7 2021, 11:56 AM

That is why I mention #1 is easier, will do the job in terms of visual purposes although not that serviceable. Just buy hard mesh from the hardware shop. You don't need to do woodwork. Just cut mesh/paperboard, screw secured and plaster.

This is more accurate since you are fixing a ceiling instead of a wall.
https://www.youtube.com/watch?v=yDLyrSqicoQ

6 inches to 3 inches is easier than 6 inches to 5 inches as you have a bigger surface for hold for cut and screw, just do similar as above youtube with a 6 inches board with 3 inches holes in the middle. If too difficult to cut near round 6 inches board to fill the hole, just trim the existing ceiling hole to square-ish so you end up like the above youtube example.

The plasterboard is very forgiving, just cut with a saw or strong blade and fill the gap with wet plaster. It won't visible upon dry that is why ppl use this material in 1st place...

Do note the hard part is to align the new hole in a line because this is about workmanship, but if you don't 100% particular 1-2cm off, it should be ok. if each new hole is 6-8ft apart, it is very hard to tell...

You don't need to cut those 1-2" inch support wood. Just buy precut from the hardware shop. Usually, it comes in either 6ft or 8ft at about rm2-5 a pcs.