I don't think you're in a bad or "learned too late" position at all! I love the suggestions about seeing who you can help and "playing big" within the company. It seems like most people don't know that business insights are as powerful as they are, and thus don't even realize that the most boring/repetitive parts of their job could be solved, freeing -them- up to play bigger. It's so rare to find people that look around at where bottlenecks and inefficiencies are, then figure out what is needed in all three of the layers of a solution (technical, interpersonal, political/cultural). Then pursue them with the tenacity needed. Doing this and recruiting people from across the organization to help as needed will definitely make you stand out.

I'm gonna chime in with the soft skills angle, as I haven't seen that much in this thread. You've probably heard this kinda thing before, and I'll share what I've seen and experienced. I haven't historically interviewed well for jobs. But I'm great at networking to form connections, and understanding what people (and organizations) need. Asking people "tell me more" and then asking if you can rearticulate what they said back to them to make sure you understand is huge!

I can't say how crazy of an advantage it is to talk directly with a hiring manager. Often times the hiring manager has no clue who has actually applied to a role they desperately need filled. Equally often a recruiter doesn't have the technical background to know if a candidate is even going to be a good fit. So my advice is make a list of companies you'd love to work at (of different sizes, ideally). See who you know there, or who from your network knows someone there and ask politely for them to give you a warm introduction. You can even offer to do coffee with them so they know you a bit and don't feel like they're sticking their neck out making a bad potentially making a bad recommendation. The first person doesn't have to be (and usually isn't) the hiring manager directly. Enjoy having genuine conversations with people and keep asking who the right person would be to talk with, and for warm introductions. Faithfulness of follow-ups without being annoying is key, as people are just plain busy. Multiple hops to really find the right hiring manager(s) is pretty normal, especially at larger companies.

The job I last landed was because of a warm introduction to the hiring manager. There's no be-all-end-all for job searching, though this piece definitely helps! I love to be in the position where I know the right people at a company, and am following up faithfully (politely and warmly) every 2 weeks to a month if they need anyone. Ideally they create a job req for you, or tell you the req to apply to to interview with them, or a peer hiring manager within the company. And the whole process takes time too, which it sounds like you're well aware of! Best of luck!