Hi, my daughter is into her 6th year at CLSG (year 12), and the experience has been fantastic. My daughter was also not an an extrovert by any means, but she has really developed a sense of quiet confidence and self assuredness, which I would attribute a lot of to her experience at school. There are all types of girls, and wouldn't say everyone is an alpha type, so wouldn't worry about things from that perspective.
Let me try and answer your different points:
Academically it is a high achieving school, but in no way pushy. The school are very constructive in helping students achieve their potential. The teaching is very good, with very approachable staff - in addition, they do regularly run lunchtime clinics across different subjects should children want some additional help. Another example was in year 7, where my daughter had a weekly Zoom call with a 6th form student to help with French.
Year 7 was fairly gentle (I don't know if that because we started in 2020, so peak disruptive COVID time), but tests and assessments really ramped up in year 8. I will point out that girls are not forced to go to lunchtime clinics, they have to make that decision themselves. Another thing I'd say is to trust the school and their methods - from year 8 they start to have sets for maths - just 2 levels. A lot of parents and children are disappointed when they are not in the top set, but at the end of the day they will cover the same content, just at a different pace, and many girls in the lower set achieved top grades at GCSE.
The opportunity to try new things is amazing - while they offer excellent provision in music, drama, sport (I'll come to this later), there have been countless other opportunities that have come up. See the list below of activities:
Trip to Globe Theatre
Spanish Trip to Valencia
Music Scholars Workshop
Chess Tournament
British Physics Olympiad
Girls Human Rights Hub
Gym and Dance display
City Youth Theatre
Year 12 Cambridge Visit
French Play
Young Enterprise (Entrepreneurship initiative)
The reason I've listed these, is that this is just a selection of what was mentioned in the last bi-weekly newsletter, and a drop in the ocean of whats on offer.
Finally with sports, despite the location and space constraints, sports is important part of the curriculum. There are certain sports like netball, cross country, gymnastics, competitive dance, swimming where the school does excel in and compete up to a national level. They also do play football, cricket and some other sports, but would say these are done more 'recreationally' than others, given the lack of space for facilities. They do also offer fencing and rowing, which could fall into 'trying something new' category.
Happy to shed light on any other specific questions you have.