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You are likely seeing the rust fungus due to the growing environment.
Rust Fungus will grow in a damp environment.
Good air circulation will help.
I have luck using Neem Oil as almost a preventative product in an area of my garden that my Hollyhocks always seem to get Rust on them.
Here are some articles with more information.

https://www.gardeningknowhow.com/ornamental/shrubs/esperanza/esperanza-plant.htm
https://www.gardeningknowhow.com/plant-problems/disease/learn-about-plant-rust-disease-and-rust-treatment.htm
https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm

Esperanza are hardy in zones 9-11, with some success in zones 8.

In colder climates it can be grown as an annual.

Soil conditions, maturity, or plant variety may have something to do with the comparison to neighboring plants.

Here is an article that will refresh you on the care requirements.
https://www.gardeningknowhow.com/ornamental/shrubs/esperanza/esperanza-plant.htm

I am not sure what this could be. If you can, remove it from the plant. Then you can try adding a bit of fungicide to see if it goes away.

Old flowers can be removed as they fade.
Weekly dead heading will help promote more flowering.
Cut back any dead or damaged branches throughout the summer. Cut back to healthy stem.
Prune back entire plant in late winter, before any new growth begins.
Remove up to 1/2 of the plants height and cut back lateral branches to help keep it's shape.
The heavy winter prune helps keep the plant upright and dense.

This article will help you.

https://www.gardeningknowhow.com/ornamental/shrubs/esperanza/esperanza-plant.htm

I would simply cut the plants branches by one third. This will help them to come back just fine. Here is an article for more information on the plant: https://www.gardeningknowhow.com/ornamental/shrubs/esperanza/esperanza-plant.htm