As the lead data scientist at a small-ish fintech, I can confirm many of the frustrations and disappointments in the OP. But my trajectory was slightly different - from being the only "data science guy" in 2016, to now leading an autonomous team of four, with quarterly meetings with the CEO, and monthly meetings with our tech leadership. I decide tech stack, workflow, and hiring. Execs decide priorities. Sure, some of it was dumb luck, some of it was actually having a CEO that cares about data strategy, but I like to think at least some of it was me.

So here's what I think I did right:

1. Provide indisputable, obvious business value every month. You should consider yourself an in-house consultant to whichever cost center your salary is drawn from. If you're product development, prove value to them. If you're operations, or sales, or marketing, prove value to them. After about two months, you should be able to justify your existence in two sentences. Just remember, most of your company probably thinks of you as a optional add-on.

Your first few projects should attack high-impact pain points with the simplest solutions possible. My first projects were basically ETL into some basic regression into a dashboard. No machine learning required. But it was better then what they had (which was often nothing), and it was STABLE and RELIABLE. And that leads to the next point...

2. Build trust. With my dead-simple models, nothing ever blew up, there were no nonsensical answers, and there wasn't much brittleness when new categorical features or more cardinality was added. It mostly just worked. And that built my reputation for me. They didn't have to understand what was going on in the model, but they knew, from experience, that they could trust the result. Once I had the credibility, I could start building more complex, more elaborate models, and asked them to trust those as well. If they don't trust your models, then no business value has been created, and your job is worthless.

3. Recognize that data science is being done everywhere in the organization, and respect it. Every department has someone who has built a monster spreadsheet that contains more embedded domain knowledge then you could hope to learn in a month. As data scientists, we like to think that we're helping the organization by building critical metrics to improve performance. But here's the catch. If the metric was truly critical, someone has built it already. It might be ad-hoc, use poor-methodology, and be somewhat wrong, but it works and is good enough. You have to find that person, learn from them, and improve on it.

4. Be as self-contained as possible. Ideally, your critical path should not depend on other teams doing things for you (except for IT setting up data access). You should be able to do it all. From front-end dashboards, to ETL, to DevOps. Remember, you're an in-house consultancy. You should be able to take problems and just handle them, rather then be a perpetual bother and distraction to other teams.

There's more, but if you do these four things, I think you can build the reputation in your company for creating useful, accurate data tools that help other people do their jobs better. After that's achieved, people will breaking down your door to get your help. That's where my team is now - we've got a backlog for at least 18 months, with our work priorities often being set directly by the CEO.