(Starting with a caveat that I've only worked with teens, not lived with one of my own, so please feel free to ignore any suggestions below because hypothetical parenting advice is usually absolute nonsense, but in my defense it was my job to work with 11-13 year olds so I have a working knowledge of the species!)
The teenage years are really hard, and I can imagine it all feels quite perilous.
Just some thoughts ot questions i woukd be asking myself were i to be in your position:
You could initially consider whether she has any capacity to act upon any information that she is given- does she know where any of them live, surnames etc, and is there a likelihood of her seeking them without you? what would she do with the information? Some kids would be all over social media trying to find them, some would be angry with you in person, some would be delighted and excited but handle it really awkwardly. What do you think your daughter might do, and could she do anything that might compromise her safety? Does she really like the idea of siblings and would she be keen to seek them, or possibly even resent you for not adopting them? (in the way that teenagers who have no idea how these things work in real life so often do find things to resent!) That would be affecting how I gave that information. However, I would definitely be looking at telling them.
Also, in terms of contact, do they mean letterbox? Phone? In person visits? Do you know anything about them, or what they expect? Do you have a preference for what contact would look like? that would be shaping a lot of what i would be looking at telling her. Having her write a letter to a little sister is marginally less fraught than a weekend away with 3 siblings all competing for attention.
Having worked with fostered and adopted teenagers, I agree with you in that I suspect it will be hard to find a "better" time to tell her- in year 8/9 they are choosing options and are hormonal, but year 10 they are doing mock gcses, year 11 is exam year.... and it all coincides nicely with both a surge in personal freedom and a dose of hormonal angst that makes reasoning with them logically a pipe dream. Teens can take different amounts of time to process stuff, so if you know how long her processing time might be, you want to avoid the worst of it during exams if you can.
I can definitely see waiting until a holiday rather than during term time, but I would say that you probably need to tell her something one way or another. I would worry that someone would accidentally let it slip, or that she would find out from someone/somewhere that you knew and didn't tell her and that would damage her relationship with you because she would feel like you wouldn't trust her with important information. From what you have said though, I suspect you know that you should tell her, but I would agree that thought and care needs to be taken in how to do it
If you are going to tell DD, is there any way you can draft in support networks of school pastoral staff, adoption support fund, therapists, etc to support her as she processes the information?
If you decided to tell her, you could just do it outright, or you could maybe have a strategy over a month to drop in key bits of information to "test the water" gently in a way that escalates the amount of information but in a non threatening way.
For example, you could start by retelling a funny story about siblings from your own childhood, then the next week letting her "overhear" a conversation about BM between you and DH wondering whether she had siblings of her own and if BM ever wanted siblings for DD, next week dropping in a reminder that you are writing to BM and expect a letter back, the the next week wondering whether DD might like to start contact if it were to be an option, etc. That way you aren't committing to anything specific, but can gauge her reaction. If it is all positive, you can move on and let her know faster, of she reacts badly or says something tricky you delay the next step and unpick what she has said, allow her to process it and come to terms with it before moving on. I've found the "jug ears" strategy sometimes works well with teens who need to be introduced to ideas slowly or with plausible deniability built into the interaction.
Personally, I would be keen to get all my ducks in a row before divulging anything to her, but i often find a delay in itself is only useful if it is used to gather resources because I assume that someday she will find out, and a simple delayed telling doesn't necessarily equip her with more tools. I would be inclined to see it as a when not if you tell her, and any delay as a way to plan relevant support. That way you can honestly hand on heart say you told her all you knew as soon as you could in the most emotionally safe way possible for her. From what you have written, nothing seems to be happening for a little while anyway so you and DH have plenty of time to corral anyone you need to into supporting her (and you.)
Whatever you decide to do, and however you decide to do it, as long as you do it with clear intentions and have a realistic, honest plan for how and when to tell her at some point, and aren't just kicking the can down the road, you can't be criticised for that. Well, you can because teenagers would criticise a piece of string for being too stringy if you asked them, but you know what I mean!
Good luck!