It’s hard yet can also be great to have a work experience student in the room. I have only had two, and certainly the first couple of days were a bit tricky as to the children they were a stranger. The other trouble is, unless you’re in the last couple of weeks of summer when so much else takes over, the teacher still needs the children to be learning, completing work…..and as a teacher the pressure of handing a group to an unqualified inexperienced teenager to complete their work with can be too much (and I say this as someone who started, like you, by doing work experience in a school at 15 and wondering why I didn’t have more exciting jobs to do).
I used my work experience students to do things like unofficial interventions, an extra intervention session if you will, mostly social ones where they were playing a game (extra doesn’t hurt) and it was interesting to see in terms of how the student reacted to behaviour and how they interacted. Yes, they were also asked to clear up messy activities or indeed do things like manning the art area in choosing time (under instruction and direction).
One thing to note is some schools are more welcoming to students and trainees than others. Just like some work places are better than others.
I have no idea about apprenticeships for being a TA at 16 but thinking about it I also have not seen an employee at a school who is under 18. Nurseries, yes, worked with many apprentices over my career.
No harm in applying though if you see them advertised.
What school year are you in? My guess would be Year 11 based on what you are discussing - I recommended you also seek more work experience (at a different school) for the gap where your GCSE’s have finished, and possibly consider some volunteer work with something like Brownies or such to boost your experience, and your confidence in yourself.
Do not be disheartened if you cannot find an apprenticeship for 16, apply for college level 3 as well as back up, or consider early years apprenticeship level 3 as a step.
My last piece of advice is don’t take anything from work experience personally. You are not an employee so will not be treated as one. The work can be arduous (like cleaning) because there’s little they can actually allow you to do. But do try hard to use your initiative and be proactive - See things left in the wrong place? Blunt pencils? Paint pots that need washing.? Books left on the floor in the book corner? Do it, wash it, tidy it, you’ll be appreciated and may well even be asked back or considered when jobs start to appear if you have done a good job and have shown a good work ethic.