Sadly not hot enough here to grow Papaya so I can only draw on my experience of growing other fruit in pots to offer some ideas of what might be happening…
I think the fact it gets droopy leaves and revives after water is a clue it might not be in a big enough pot? I find that most fruit trees benefit from being repotted each year. If space permits, moving them to a bigger pot gives them more root space - and bigger pots will also hold more water to keep your plant going during the day. Repotting also enables you to add fresh compost and nutrients (eg worm compost or slow release fertiliser). The fact that some of the leaves on your tree are yellow might be an indication that it might be low on nutrients.
My last thought is that if lack of water is an issue for the plant, you may want to remove the other plant in the pot and replace it with a mulch of bulk or stones, as this will help retain moisture and reduce competition for nutrients.
Anyone else have any ideas to help Fen?
EDIT: one way to tell if it has outgrown its pot is to put the pot and tree on their side and gently ease the tree out of its pot. If you can see the roots in a mat all round the sides of the pot, it has outgrown its pot - and either needs root pruning or putting in a larger pot.