Welcome to the Bunnings Workshop community @namrah. It's a pleasure to have you join us, and many thanks for your questions about repairing vanity doors.
It might be worth investigating whether you could replace the door as any fix that I can think of would likely cost a good portion of a new door. The internal medium of that door is either MDF or chipboard, and both of these disintegrate readily when exposed to water. As you can see, the coating is already delaminating, and it's a sign that water has significantly penetrated the board. When water comes in contact with MDF or chipboard, they swell, and there is not really much you can do about that at this stage. You'll find Kaboodle doors have a thermal vinyl coating with no exposed corners to prevent this from happening.
You might like to read through these previous discussions:
You could attempt to fill the gaps with Selleys 8ml Araldite Ultra Clear Epoxy Adhesive and then clamp them closed, preventing more water from entering. Alternatively, you'd need to remove the damaged laminate, dig out any disintegrated MDF/chipboard, fill the damage with Builder's Bog and then paint the whole door.