Should all be ok, once you make the repairs.

And obviously put a tray under the bleach the next time

Yes!

So sorry this happened to you. Once you do your repairs, I suggest you purchase several “Watchdog Water Alarms”. They can detect even a drop of water / liquid, and the alarm goes off. It operates on a 9-volt battery. I have several in all of the bottoms of my sink cabinets, one near my washing machine floor and one in the pan of my hot water heater. Watchdog Water Alarms have great reviews. I got these after we had hot water heater leak; thankfully we caught the leak when it first started.

You can probably cover up the hole with some peel and stick floor tiles. Rinse it with water several times and let dry (leave doors open) scrape off any loose stuff so the tiles will stick nice. I put them under my sinks in kitchen and bathroom. Also did some kitchen drawers and shelves in kitchen rather than that stupid contact paper stuff.

That's probably a total fluke that the bleach container leaked. I can't imagine it would happen a second time unless you store pointy sharp things under your sink.