If the benchtop is chipboard, it's not really something that could be repaired easily. The cost of having someone repair it for you would be well on the way to the price of a new benchtop.
Once a laminate benchtop starts bulging the internal timber has swollen up from moisture. There is not much you could do about the bulging and the benchtop is likely nearing the end of its lifespan. You could disguise the torn out section so it looks nicer. I would suggest taping off around the area and applying Builders bog to fill the section. You can then sand the filler back so it is flush with the benchtop and then paint. We have the Dulux Renovation range which includes a laminate benchtop paint.
You should find this step-by-step tutorial helpful: How to paint a kitchen benchtop with Dulux.
In my house, I have this problem. The laminate has now cracked as all the supporting chipboard has disintegrated away. I'm in a rental property, and it is not something the owner wishes to fix. The damage to mine, I believe, was caused as they previously had a very short-necked spout on the sink, which allowed water to splash onto the tiles and then sit on the benchtop. They also didn't space out the first row of tiles from the bench, and there is no silicone seal to prevent water on the bench from creeping under those tiles.
In the past, I've considered ways to halt the ingress of water, at least. This can be done by removing all the silicone along the sink's edge and replacing it with a new bead of Selleys 300g Wet Area Waterproof Silicone Sealant - Clear. It would be best if you removed the sink entirely and laid a fresh bead of silicone under the sink's lip.
If the damage is near a sink, you would be advised to remove it to give you an idea of how bad the damage is. You could then potentially dig out any disintegrated chipboard and then paint the remaining with exterior PVA glue to bind it. To add some rigidity back to the bench, timber blocks could be inserted into the bench's thickness and glued in place.
Personally, I'd consider spraying a small amount of Bostik 500mL Expanda Foam - Expanding Foam Filler into the eaten out void, then cut and sand it back into shape. This foam does expand quite dramatically, so you wouldn't need much. Once the repair was completed, you'd silicone the sink back into position. - MitchellMc
My suggestion is to go to a stainless steel (SS) specialist and have a “cover profile” made for the rear of the sink (that will cover your damaged laminate. Draw a template of the shape of the rear of your sink and take detailed measurements. Get the sheet stainless steel folded so there is a bend at the back corner that goes up at 90 degrees over the existing tiles. A ‘mini splashback’ if you will.
When you insert the SS under the lip of your sink, use silicone to fix the SS and also to stop any water getting under your sink. The “lip” at the back just goes up against the tiles and will stop water from running down the tiles into the cabinet. This is also a gr8 way of retrofitting a smaller sink in a larger hole by using the SS to “fill in” the gap at the rear of the sink. - Peejay2
Once water has now gone in between your actual benchtop and the laminate cover protecting it, it will only be a matter of time before wood rot settles in and begins to disintegrate your benchtop where the water damage has occured.
To temporarily fix the issue while you gather your funds for a new benchtop, you can use Selleys kitchen and bathroom silicone sealer. You need to remove all the old sealer at the back of the sink and apply a new seal. If the laminate is now loose you could try to dry it off with a hair dryer to remove excess moisture from the area. I don't know how long a repair will hold. Head into the store and get a quote. You might be surprised that the replacement cost is actually quite reasonable. - redracer01