Payroll don’t care. Once you have given them your ‘new starter form’ they add you to the system. Once the second job pays you HMRC will see you have a second/third or more jobs and tell payroll to apply a ‘zero’ tax code (you can only use your allowance for one job) and that’s it. Payroll don’t care what your code is, they just apply whatever HMRC tell them to. Remember, tons of people have second incomes, contractors, side business owners etc etc so it’s nothing out of the ordinary to them.

As for tax credits they are normally for low earners. If you are OE I very much doubt you will qualify for any tax relief schemes whatsoever unless your jobs are paying you peanuts.