I am an L4 engineer with decent knowledge of my team's stack.
What are some actions I can take to meet expectations in my current role for the next few years, while minimizing the amount of time I spend on work?
Given that I'm not shooting for a promotion, does that change how I should approach relationship building with senior folks on the team? There is a lot of advice on Taro about relationship building, but it appears to be aimed at folks who wish to promote quickly.
I'd caution you about conflating "I don't want to get promoted" (this is fine) and "I don't want to do well at work" (this is stressful).
Most of the tactics around relationship building and project selection should still apply in your case. In some ways, the relationship building part is even more important: my advice for minimizing your time commitment at work will likely come from leverage in two areas:
Depending on how much you trust your manager, I'd also tell them about your desire to not get promoted, but emphasize that you still want to do well. Most managers will be supportive, as long as they feel you're able to still deliver high quality work on time.