The biggest political capital that you can build up is your technical understanding & skills. But they are only useful insofar as you put them into the context of the broader company strategy. Giving appropriate advice, and delivering, in the interest of the company, will give you capital, i.e., people listening to you & relying on you, trusting you, which gives you power to steer. Preparing contingency plans & pitching then, then executing them, is the best way.
Depends on the scope. Simple things might be docstrings or sections in READMEs, bigger things issues/tickets or a page on Notion/Google Docs or whatever you use; overview there or in your head.
The crucial mindset imo is that you're trying to do something that's already useful. At the time you write these things, you're probably more familiar with the topic at hand than anyone else in the company; try to leverage that into writing a document that someone else (or yourself in the future) can save time once they actually execute what you write by getting faster to the point where you're at right now. E.g. from the article, rewriting a js package structure in vite; think through implications and potential hurdles you already have a solution for.
They're useful in almost all outcomes. If they won't be executed, at least you know why (e.g. too complicated/effortful), and if they're executed, best case you can improve the company's offerings substantially.