I know the Scrum Master must have observed this, because it's obvious 3/5 days a week at least.
As a member of this team what can I do from this point?
You should keep doing your good work and performing professionally during stand-ups (as you are already doing).
As you are not this person's manager nor scrum master there is nothing you should be trying to fix or correct on them. In fact, this doesn't seem to prevent you from doing your work at all, and is "just" something that demotivates you a bit.
You say your Scrum Master most likely has noticed this attitude, so on that matter I would leave it be and let your Scrum Master determine how to handle or approach this person's attitude (unless this starts to physically prevent you from doing your job).
why should I care (I'm also a Scrum-cynic) if Anne doesn't and faces no consequences, maybe just because I'm newer to the org than Anne?
You should care because you value your job, as well as the level of professionalism and quality of the work you deliver.
I know this person's attitude may be a bit demotivating, but I suggest you don't compare to others in terms of the quality of the work you have to do. Instead, try focusing on your own professional development, and chose to keep doing a good job.