I’ve been asked for references when setting up a contract with a school, but not when dropping in to do an observation for a case where I am contracted with the parent. I agree this does sound excessive. I can understand providing my DBS and qualifications checks, but otherwise…..
I haven’t worked for an independent school before though, so their procedures may be different to LA schools.
I’d definitely check in with the Head Teacher as you may find HR have been given the heads up that you will be working in the school and have just presumed you need to fill in the forms for recruitment.
Good luck, and I’d be interested to hear how it turns out.