There are three iOS apps on iNaturalist:
- the original iNaturalist app, or iNaturalist Classic
- the most current iNaturalist app, known as iNaturalist or iNat Next
- Seek, which is probably not what you’re looking for
The feature to add projects to observations using iNat Next is upcoming from what I know. It certainly doesn’t exist yet, and when I’m on mobile I very much have to go to the web version on my browser just to do things like reorder photos, add annotations, add observation fields, and add them to projects. I hope it happens soon.