Points 1 and 2 describe the jobs of most Staff Engineers (or higher) at large tech companies like FAANG that I know. Smaller companies rarely have these because, perhaps unsurprisingly, small shops rarely have big enough technical challenges to need more than 1 person like this, and they double as management.

3 is likely to be a sticking point however. Once you have responsibility for large projects you are often in a certain amount of resource contention, the chance of avoiding political battles there is small unless you are a known superstar within the company.

If you're ok with that, I'd prepare for a whiteboard interview at one of the big well-paying tech companies.