Ways to provide value to people further in their careers who help you?

I love this question! We actually gave a masterclass about this topic, which I highly recommend if you haven't seen it already: [Masterclass] How To Build Deep Relationships Quickly In Tech

I've been on the mentor side, and I have worked with what's close to the largest gap: I mentored several new grads engineers while I was a tech lead. Here's how they added value back to me:

• Extreme gratitude - The people who are really deep into mentoring almost always have some degree of altruism and just want to see people be happy and succeed. As the mentee, the simplest way you can satisfy that is to be very appreciative and show positive energy. There's really no such thing as thanking someone too much. You know how at the end of movies with a mentor <-> mentee pair where the mentee gives some heartwarming speech at the end deeply thanking the mentor? All my new grad mentees have shared some version of that with me. 😊
• Offloading my work - When I was swamped (happens a lot as a tech lead), I was able to delegate more straightforward coding and project management tasks to them. Eventually, these mentees started asking me proactively if there was anything they could take off my plate. This is mutually beneficial as what's easy for a tech lead is likely still a learning challenge for a junior or mid-level engineer.
• Got me stuff - This one's pretty straightforward: They bought me things, usually food. One of my main mentees treated me to an extremely nice dinner after my mentorship had helped them grow from junior to senior at a lightning pace. The final bill was over $200!

If you're interested in the mentor side, here's my in-depth case study about it: [Case Study] Mentoring Junior SWEs [E3] to Senior [E5] In Just 2.5 Years At Meta

Adding on to Alex's great answer, I think the biggest thing is simply to follow up and let them know how you're doing. Talk about how their advice was helpful, how that impacted the decision you took, and the result of that.

For most mentors, their satisfaction comes from knowing that they helped someone. Tell them about your promotion or new-found clarity.

Beyond that, in a work environment, one powerful thing to do is thank your mentor publicly. When you hit a milestone, acknowledge them in your email, or tell your manager how much they helped you. In many companies, this can help your mentor get promoted, which is obviously very valuable for them.

What Alex and Rahul have mentioned here has certainly been a good add. I just want everyone involved to be happy and really successful. If you can take work off my plate that is always really helpful. If you can keep project timelines going and make the business successful then all better. Now if you have fun, accomplish your dreams, and help others do the same, then you're all good to go. Good luck to you and I'm always game to network if you want to reach out.

On choosing the right mentors:
I think it is good to try and get the lay of the land at your team/org. I have learned that not every senior+ engineer wants to mentor (i.e. there are those that genuinely enjoy it and those that do it because they have to). Try prodding your potential mentors with your question(s) and see how they respond each time. There will be some that will respond in a way that unmistakably show they're not only answering your question but have also thought about where you might be coming from. Personally, I would gravitate towards these people because in their answers, I know they are getting value and personal gratification out of helping me. I bet they are not difficult to make conversation with either.

On nourishing the relationship:
I love what Alex said about extreme gratitude. This starts from your first message, I try my best to not come off as someone who just wants to extract information and having a consumer mentality. Sometimes I overthink but I endeavor to make my messages considerate and friendly (I like emojis), and then I take the time afterwards to thank them (e.g. "thank you ____, that cleared up a lot for me and now I understand why ___."). But be optimistic and assertive about it! (We don't want to get obsequious, at least in my opinion.) I think keeping your conversations lighthearted and appreciative is one of the easiest ways to build rapport.

On thanking them:
I love what Rahul said about publicizing your thanks and telling your manager about it. I had a senior who would go out of their way to mentor me and I would always tell my manager. I think this person was diligent with almost everyone though, they were promoted pretty quickly.

This is all from my personal experience so far but I hope you find your people :)