In the short run, I think I would just tell her (while she's not upset) than when she runs into her room, you will let her have some time to herself to cool off. (That's actually a pretty positive response my grandson sometimes has to his own frustration or disappointment.) As soon as she's calm again, she can come out, and you'll always be happy to have her with you.
And at 2 1/2, she's not "behind" in potty training. If you're pushing that and she's not able to respond, it will just make the process slower, more complicated, and more unhappy for all of you.
A most important thing I've realized about ALL human behavior is that it's all a means to get our legitimate needs met. Defiance, whining, pouting, tantrums – also affection, snuggling, humor. Any particular behavior may not be a good strategy, and for little ones, it's often a bad strategy. Children get angry, slam doors, scream – not as a deliberate, planned manipulation, but as an intuitive way to try to meet their own needs. And depending on the response or results they get, these behaviors may stick around or eventually go away.
If your daughter senses that she has hooked you emotionally, she feels powerful. Even a negative reaction from you tells her she's had an effect. When this occurs at a moment the child is feeling very little power, it's very, very attractive. She'll gratefully take power and control in whatever form she can find it.
Before deciding how to deal with her new behaviors, I'd try this: stand in her shoes and consider life from her perspective. Notice all the frustrating, controlling, maddening and discouraging situations for a new little person with very little autonomy and limited language skills. From there, you might find creative ways to reduce as many of those frustrations as possible. This in turn should reduce her negative strategies to deal with her own frustration.
I'd be really, really careful NOT to intimate that your daughter is wrong to feel her feelings. She really doesn't choose them, they choose her depending on the situation. Anger and frustration are natural, and completely legitimate from her point of view. If you discourage them by shaming or punishing her, the feelings won't go away, they'll just go underground and emerge in some other way.
You might make a little set of cards, as a project to do with your little girl, that she can show you when she has trouble expressing a need, whether a feeling like "angry" or "frustrated," or a physical need like hunger, or any other way she usually needs your help. As you do this, explain that you want her to be able to show you what she needs. (Cards like these are already available for kids with speech delays or autism; you can probably find them online if you don't want to make them.)
I can almost guarantee that she'll be surprised and grateful, and may respond with more "communication" and less door slamming almost immediately. I'm NOT suggesting that you drop your role as primary authority. She will still need clear boundaries just to feel safe. Just boost the empathy factor – kids hear "No" and get punished more than is usually necessary, and react against it.
As you reduce your daughter's frustration level, you'll reduce her reactivity, her need to feel angry, hurt, or defy you. Thus, you'll also reduce your own frustration and reactivity as she feels more cheerful and cooperative. Your little girl is acting out of her frustration, it's what little kids do until they know better, or are given other choices by the adults who control their lives.