Alright so!
There's some strategy about it, obviously, and she wants to work with a mental design as much as she can, if she's going to be using green. but she wants to - do it in as much as she's still - thinking about earnestly what she hopes would help? She remembers poking her powers early on, and that seemed like such a big and daunting ask - to have something earnestly and freely given to use to forge a better future - and probably a lot of the impact of that is about it passing through more hands, but she still... wants to give it its' due respect, you know?
And what she earnestly thinks would help - not just help her (which mostly is going to swing on it being impressive and notably thoughtful), but help the queen - is... something more social? They have an identity as warriors, yes, but realistically they've been curled up in their cozy warded paradise for thousands upon thousands of years, without too much more fighting then festivals and a few small fights relating to the occasional magic using supervillain, or the very very edges of WW2. She doesn't need tools to fight, for all that she's pretty sure they're a sign of prestige and honor and respect and all that in their culture. She sketches the basic idea out in bullet points, then goes and thinks and feels it through.
So. The most basic part of it is going to be... connections. Hope doesn't connect quite as clingily or aggressively as love, but that's okay. She's not looking to make something about - permanent connections, she's looking to make something that helps with the burden of the Queen, the supreme executive force of a noble queendom full of immortal comrades. She's looking to help her find, help her feel, help those loyal to her reach out to her, when they're feeling hopeful, when they need to reach out to righteous authority, when they need to fight for their commander and fulfill their expectations of themselves and their duties - an expression of hope as a guiding light towards the promised land.
It's shared hopes, hopes reaching out to her, a sense of prayers to the goddess-queen, the loose but legendary connections of a savior to the saved, the guidance of the hero on high to the soldiers down below. She tries her best not to make it - invasive, but make it about... what their souls present to her, how they reach out, how people come to petition her, and how she can feel out how she can fufill their hopes, in knowing them. It's not a tool of interrogation, it's a tool of - negotiation, even appraisal - to feel out the flow of the fight, to feel where the hopes spike and dim to feel how they fare, to sit in a council room and have a sense of how badly they need, in their hopeful hearts, for their priorities to be addressed and for them to be relieved and for their work to be aided. It's also... that hope reaching back, to uplift and lighten their load. Physically, to reach out and help those who are fighting for the hope she shares with them, to literally make their burdens lighter and their bodies stronger, and also to... touch their souls, and ward them and their wills with the solidarity of a unified dream.
She's very careful not to give her a mind control artifact, just something that can... reach out and reassure, in a way that only the spirit can see, sometimes, and something that can help make a barrier against some of the more... external tumults of the spirit. There's also... not not a flight system in there? It's a little bit excessive, but she's already reaching out to the world to lighten things and guide forces (albeit in a pretty indirect way) and putting two and two together is simple enough that she feels like she'd be skimping on it if she didn't include it, even if it's probably horribly inefficient to use outside of the most dramatically hopeful scenarios. There's a decent chance she can fly already, too, so having something that can help that ability with a bit more efficiently and quietly is good, too.
She's a little worried these hopes are too - impersonal? She's not even too sure that it is as much of a shining city on the hill as her monologue made it out to be, there, but - that's part of the point of it, yeah? There's a few simply practical things in here, sure - someone who is purely a shrewd negotiator or a squad leader could make decent use out of it, yeah - but the real value is... in being hopefully harmonious, unified in dreams and purpose, and she likes to think that's the hope they should be shooting for, and what she wants to help out, you know? Plus, it's just cool! She adds in some sparkly light control highlights to make it a bit better as eye-catching jewelry, and just... channels her hope that things will go well and they'll be able to build something, together, something as beautiful as her dream, here, and adds in the rush of green to make it all... tick.
Once she's done, she flops in bed and curls up with her violet core for a bit - focusing on the feeling of channeling the violet light like she had with the power, feeling the power through her blue-ier senses, and just... basking in hopeful love to help herself recharge, a little? It's probably going to be a long time before she's much of a real lantern without her tools, but that's okay. No point in not starting now!
...She's feeling a bit more than just heart-tired, now. It's pretty late. She's glad that - hope renews itself, especially when she's working with it this... directly? It's still probably not a great idea to lean on it too much, right now, and there's probably some finnicky ultimate limits to dealing with it without doing something more drastic to her brain. Still, she has the skills for some basic body enhancement, and it's not too hard to use a little green light to focus in on herself and give her a little bit of steadying energy.
After a bit, she goes and grabs some water and checks back in on if there's any new chats to her or news about the whole spaceship kerfuffle.