What role do the junior-devs in my team play in my promotion to TL of the team?
A tech lead has to, well, lead, which means that a good tech lead needs to be able to empower others by growing them and making it easier for them to deliver. This is why the mid-level -> senior promotion often contains a lot of mentorship: Senior engineers are often expected to function as TLs, and mentoring a junior engineer to mid-level is one of the most powerful ways to earn their trust and have them contribute to the projects you're leading.
How am I to approach 1:1s with juniors devs in the team
In a nutshell, just try to be helpful to them. Figure out what they want help with, whether it's building up a skill or just wanting someone to talk to. Fill in those gaps and create a vision for how they can make the jump to mid-level. We have 3 great resources on how to do that (shortest first):
What does it mean to gain social capital in this interaction
"Social capital" is a fancy phrase for trust and the strength of your relationship. The more social capital you have, the more that person will be willing to be honest with you and help you. Social capital is extremely important for TLs as TLs have to align people and want people to listen to what they have to say in general - This is really hard to do if people don't really like you.
How to establish influence without authority in this interaction (even if there is scope for authority)
Through social capital! You want people to do what you want and carry out your vision not out of fear or deference to your title but because they genuinely like and respect you. This is why mentorship is so powerful - If you mentor folks properly, they're going to be very loyal to you, and when you say "Jump", they will immediately ask, "How high?".