My Daughter, is very much like your Daughter... even the multilingual part.
My Daughter, in large groups, can be "shy". BUT... the thing about her is, she is very observant and cognizant of others and can analyze people VERY well- better than most adults. SO, her "style" of engaging is just different from other kids who are usually more loosey-goosey and not as focused and are usually just irritating others. SO... we "value" the personality my Daughter has. That is "her." We always emphasize with her, that she ALWAYS be her SELF... and to always be proud of who she is... because she has a strong grounded sense of identity. So we focus on that.
"Shyness" is pegged as a "bad' word as a child is growing up. Its a stigma sometimes... if told to the child too much, it can give them hang-ups.
To me, "shyness" is not a bad thing. It is something that a child goes through... and being so young as your daughter... they change as they get older. I myself, was "shy" as a child... but as I got older, I got more outgoing and very outspoken even. In college, I "blossomed" even more... and my Professors would always tell me "Susan, you are the life of the class and the only one who says her mind and you are very informed... but give the other kids a chance to show t heir voice..." I was a straight A student... my previous "shyness" as a youngster, was a distant memory.
The MAIN thing about a child... is that they have (1) confidence (2) self-assuredness (3) self expression (4) self Identity (5) good communication (6) good social evaluation & character (7) self-confidence.... etc. "Shyness" is not enough to drag a child down... unless they are made to be even MORE self-conscious about it from adults. And THEN, it "will" become a problem.
In Teacher conferences re my daughter, Teachers always say she is the SHINING example of how they WISH their other students are...."but" that she is shy. For me as a Mom, it does not bother me... because I KNOW my daughter. She is wise and mature and outgoing in other venues and smaller groups. BUT, in time, she will mature more and get more adjusted to "large" groups that she is a part of. NO biggie.
I would not "force" your girl to be not shy. There is a time and a season for everything. In time, she will not be that way... or will grow and blossom in other ways.
MANY geniuses & talents in the world, are actually introverts... it never made them any less of an achiever.
Being "shy" is not a "problem" unless it is destroying all social aspects in your daughter's life or disrupting it. AND, as a Teacher, (in my daughter's case), they just call on her a tad more... or have her do "errands" for them with other Teachers, or have her do verbal instructions for the class etc. And- as for engaging in peer-play as you said... each child has their own personality.
The "school" or Teacher is not the SOLE entity that "has to" build her confidence. A lot of it comes from home too... but allowing for the child to build upon their OWN strengths... not trying to be someone else... which will only make them shyer and more self-conscious.
For me as a child... the more my Mom "made me" try to be "outgoing" the MORE I withdrew... I HATED her doing that to me... it was not "me." It was her trying to make me into her. As young as I was... I KNEW I did not have a "problem"... I was just on the quiet/shy side. I didn't know WHY on earth she'd tell others "Susan is shy.... so..." and then sound like it was making excuses for me when, WHY does it have to be "bad" to be more shy?
Your daughter has LOTS more years of childhood to blossom...
All the best,