Prodigy doesn't allow too much interaction with the database, as explained here, because it easily gets messy. If users are able to make changes to annotations, you probably also need a way to track who made what change and when.
So instead, here's how I've dealt with this in the past. I make two datasets, say ner_v1 and ner_v2. When I start annotating, everything goes into ner_v1. I'm fully aware that this v1 data will be a first draft. Many annotations are correct, but some might need to change later after understanding the problem better.
Then, once there are a few flagged examples, or when some bad labels have been detected, I re-label the relevant candidates and move these annotations to ner_v2.
Then, when it's time to make a model, I have a custom script that gets the examples from ner_v1 and ner_v2. If an example appears in both sets, I always prefer the annotation from ner_v2. This gives me a final dataset that can be used to train a model.
Other people might have another way to handle their data, but for my projects, this approach has worked quite well.