All of it. Nothing in the payroll cycle is available only in the app.
Payruns and payslips
Payruns live at .../payrun/, with payslips beneath them carrying the detail of each line, the PDF download, email sending and a refresh endpoint. Journals and payment files sit at .../payrun-journal/ and .../payrun-payment/, including submission of the payment instruction.
HMRC submissions
The FPS at .../rti/fps/{tax_year}/, with submission, a late-reporting reason, lookup by payrun and a flag for a submission sent manually. FPS corrections, which can be promoted to a new FPS. The EPS at .../rti/eps/{tax_year}/. CIS300 returns and subcontractor verification for construction. Your integration decides when each submission is sent.
HMRC notices
Notices HMRC sends you through the Data Provisioning Service arrive at .../dps/. You can apply a P6, P9, SL1, SL2 or PGL1 through to the employee.
Everything around the payroll
Employees, leave and statutory pay, opening balances, National Insurance summaries, pensions and auto-enrolment with contribution submissions, benefits, statutory documents (P45, P60, P11D, P30, P32), webhooks and employer settings.
Where is the full list?
"Payroll API resource map" describes each part of the API with a link to its reference section, and the complete reference is at https://payroll-api.moonworkers.co.uk/api/redoc/.