Paint will not stick to silicone.
You will need to sand it all off, be sure you do not leave any silicon on the board.
If you need to do more patching use an exterior Vinyl patching compound
Patch, sand , prime and paint.
The recommended, long term method
There are quite a number of places on line that sell repair parts for all types of home appliances.
It will likely be easier to purchase and install the proper replacement part than to attempt to repair a part.
Using your favorite internet search engine, look for
replacement parts <make> <model>
Process is similar to but not the same as drywall -- you patch with the material similar to what the surface is made of.
In my case, I had to patch holes made by an electrician hunting between consecutive ceiling joists for active wires. The electrician used a hole saw so I had the discs to put back in, albeit now slightly smaller. If you're just repairing ...
(I was lucky with my last cooktop - it was slightly smaller and my plumber was able to cut the counter a little bit to make it fit.)
With a stainless steel cooktop, I would look for stainless steel - or at least "shiny metal" to match. Something like this one on Amazon:
Definitely measure first! If a filler piece is too long, you can cut it down, ...
I put hydraulic cement over the cracks. Wish I hadn't since both of you gave better solutions, I just forgot to check the dang website and we had a storm coming today so I wanted just used what I had around the house. Didn't wanna leave you hanging. Next time around, I would look into your ideas.
Plain old mortar (or concrete with only small aggregate) would be my choice - it does not need to be a perfect seal. If it's dry when you are trying to do the work, pre-wet the area you are patching for a better bond. You'll also want to scrub off as much of that decaying organic material as possible. Use a fairly stiff mix and beat it into place.
It needs ...
If the tube has melted you better find out why? It's unusual for that to happen.
That being said, I can't count how many hoses, radiator hoses, PVC pipes i've fixed just by wrapping black vinyl electrical tape around the ruptured part. Don't skimp on the tape and pull it tight. Add two or three layers.