Recently bought a overbred unit which requires you to drill a hole above the wardrobe and wall. Then you need to add this L shaped metal piece with screws In where the holes are. To stop the wardrobe from falling if pulled on with a little bit of force.

The walls are plasterboard probably a gap behind it then reaches the brick I'm not sure. What kind of plasterplug is suitable?

This one or maybe This one ?

Neither! Plasterboard to too weak for this job.

You need to find the wood to which the plasterboard is attached and screw an ordinary woodscrew into that.

You can find where they are with a metal detector which will pick up the nails used, or by tapping if you are lucky. if this is behind the wardrobe where it can't be seen, you can also find it by a few trial holes which you can repair with filler.

If there are two uprights behind the wardrobe, use two brackets. You can buy something similar at Wickes or B&Q. A flat bit of metal bent into a right angle with screw holes in it.

The Self Drill type (Your second choice) with the heavy screw thread will hold that. However if you're at all concerned, then Spring toggles are the way to go.
If you ask the nice man at the DIY shop, I'm sure he'll give you good advice.

I'd go with @Ex on this one, free-standing furniture can stand for years without falling down but when it does it can be fatal. Screw it into something solid like the studs not just the plasterboard. On occasions I've used a long screw to get it all the way into the brick when the stud wasn't convenient.

Theres a good video on you tube where the guy tests all the different types of platerboard fixings. i was surprised which one was the best but cant remember think it was either the standard plastic or the toggle one. The metal screw in ones were the worst!!. Sods law if its dot and dab plasterboard as may not be any wood battens or studs behind. Ive fixed a book case just with an L bracket at the top as it cant be seen. .

This is one i watched https://www.youtube.com/watch?v=iJWGmPkS-Fo but there are others not as long

The spring toggles could be improved enormously if they put even a small amount of flats on the edges. I find that if you go back after a few months you invariably find they can be tightened up a bit because the thin edges have cut into the plasterboard, If you tighten them too much the wings cut two channels into the plasterboard and weakens it. I also don't like having the spring toggle's screw floating around in a huge hole, I guess this can be useful for final alignment but that's a separate issue from strength and reliability.

The rivet type ones with the setting tool are similar to some blind fittings used on metal and I've had a lot of trouble with the metal ones in the past. However they would be my weapon of choice, the ability to undo the screw without losing the fastening outweighs the spring toggle's strength. Having a proper collar fitting inside the plasterboard hole is also a positive, adds to strength and reduces deterioration caused by movement.

Its very rare I've put any form of plasplug in plasterboard, they exert forces sideways and so crumbles and pre-stresses the very hole where its supposed to be supporting it.

I've often put a batton across studs to screw things to, its not always possible but is probably the best solution.

I don't think I'd be able to sleep under an overbed unit unless I knew it was well secure.

I am more than willing to have a look for you and give any advice no charge. I am a time served joiner and have seen to many disasters.

There is a recommendation not to have overhead units but they are still made and supplied by bedroom companies.

You will also find that not one fixture you purchase has any form of insurance / liability rating only a max load.

Give me a call if you need a hand 07889 133293.