Ophelia and Bianca dont provide Pet progress when fighting them. Its not explained well im the current version, but the upcoming version forces you to dismiss your partner.
You can give the Pets food and drink items to increase their progress and also take them on a date at the Humilem Bistro, in Humilem Village.
Theres also an infinitely spawning Slimegirl you can fight inside of the brig of the Ruddy Raider (pirate ship) that you can fight for Pet Progress.
You should be able to sell your items to Ophelia, if I’m not mistaken,