Most, if not all, existing legal frameworks do not recognize anything other than a human to be a person- at least in the typical sense*. Algorithms do not have rights, legally speaking.
There are some really interesting philosophical questions surrounding self-aware AI and rights, but no government is prepared to answer those questions right now.
There will be controversy and years of debates determining how to handle a self-aware AI. This is not as cut-and-dried as slavery, as that AI was just a regular piece of software when it was created. Self-aware AI rights will most likely fall somewhere between animal rights and human rights, but since no self-aware AIs exist yet, no legal framework is prepared to deal with it.
Likely, the company would own the software that defines the AI and the hardware it runs on, but not the data that makes up the essence of Amara (which is incredibly nebulous and impossible to define). This raises some other interesting questions: is shutting down the server Amara runs on and deleting her data murder?
Even if Amara were legally determined to be a person, that doesn't necessarily imply that she would have authorship of her works. It could be considered a authorship-for-hire situation, where the company retains the copyrights of her works. It might also be considered a legal guardianship and have a similar effect on copyright (a minor can hold a copyright but cannot legally defend it in court). The company in any case would likely have power of attorney over Amara.
Realistically, without self-aware androids living among humanity (fueling empathy in the masses), there won't be much of anyone to make the case in favor of AI rights. The company's lobbying will almost certainly be enough to overcome any pea-sized opposition, and thus Amara will remain property of the company for decades.
* Corporations, in many countries, are classified as legally distinct entities and called "persons", but they can be bought and sold just like property, so they aren't really people. If they were people in the same sense that humans are, you would be charged with negligent manslaughter for allowing your corporation to go out of business. The idea is clearly ridiculous.