I have been a PM at a new job for 6 months. Since starting, it seems that everything I suggest or recommend is not wanted. My supervisor said that she doesn't believe in a RACI chart, we don't need

From what you are saying it seems that you are a part of a team that does not want change as they are comfortable with the way things are (for political or personal reasons).
You are trying to bring change there where people are not open to it and do not encourage that.

My advice would be to try to define a strategy on how to bring the new processes or ways of doing things depending on what stimulates the team. Observe how they are reacting to things and adapt to that. Plan your change management by studying your colleagues and their way of doing things. Imposing change will just make everyone even more reticent, whereas if they feel like they participated in the process and that they had a part of it, it will be easier to evolve.

Also, the best way of improving leadership overall in the company is through example. You are a leader by taking action, showing integrity and transparency and always trying to improve your work; you do not need permission to do that! It does not matter the role you have at the company, you can be the leader that you wish they had.

Some organisations have a functional, product-centred or "weak matrix" structure where PM's tend to focus on communication, coaching and troubleshooting rather than project leadership. This may be especially true of technology organisations. Why not talk to your supervisor and get her to define some short and long term objectives for you.

For what it's worth, every company has different needs from a PM. As a matter of fact I have worked at an equal number companies that do NOT care about budget as those who do.

In many cases I have made a RACI chart or stakeholder register purely for my own knowledge and use, and not as an "official" project document that I share with others. I have done this as a way for myself to understand the culture of a company and the stakeholders. However that type of document may not be required in some types of PM environments, but you can certainly do it for yourself.

Occasionally, if a particular discussion arises, I might pull out a document that nobody else knew about - just to demonstrate that I know what I'm doing and that my PM experience and methodology is much "more than meets the eye" of a non-PM.

For example, I know engineers who do calculations (and even occasionally write papers) purely for to help with their own work. All that they publish are the finished drawings, but they have their own set of documentation to record how they arrived at their drawings which they typically never share. Those documents are important for them, even though they may never be shown.

So if your organization doesn't require some aspects of PM, you may still want to do them for yourself. And if the moment ever arises, you can pull out a document to show your behind-the-scenes expert thought process (and if you're really lucky, the organization might realize that what you're doing is worth adopting on a broader scale - but don't get your hopes up for that).

With regards to "making decisions", I get that in a technical environment you don't want to be telling the experienced technical people how to do their job (even if you know better than them). And honestly it looks bad to undermine someone's expertise because they like to feel important. In this type of situation I take the question-asking approach... "what do you think about doing ____" and let them make the decision.

[side note: in an environment of big egos, I take an even more reserved approach of "playing the dummy". For example I will sit down with someone and say something like "I was thinking about this situation, could you teach me about it?" then as they are talking you could ask your question of "well would ____ be another way to approach to this situation?" and so on. That way the 'expert' may come up with 'their own' idea on why your approach is better - but because they 'thought of it themselves' they will be more apt to follow the course of action that you also think is best.]

Anyhow your feelings are not uncommon - especially at a new job. But like with a lot of PM situations, you have to consider the audience for your work. And doing a document with yourself as the only audience member is perfectly acceptable if it helps you run a project better.

-Bob C.