This is my reason for wanting a bulk add to projects:
I have a traditional project - https://www.inaturalist.org/projects/pillar-parade-s-afr - for the Lepidoptera caterpillars of southern Africa.
If everyone annotated their obs with Insect Life Stage: larva, then it would be a cinch to convert to a collection project. But very few people do, and newcomers never do. Also, some obs have more than one life stage, so they can’t be annotated at all.
So, what I have to do is go through all the unannotated lepi obs on the Identify page, and annotate them one by one. Laborious. Then I have to go to the Explore page and search for all lepis with annotation larva not in the project. Then open each observation separately to add to the project. Desperately tedious. Luckily there are several people who add caterpillar obs to the project when they review them.
If we can at least add to projects on the Annotations tab in Identify, this will go a long way to speeding up the process. And a batch add to project would be even better :-)