HMRC Self Assessment and Higher Rate Pension Tax Relief Payment

If I make a pension contribution from my after-tax salary money in my bank account, I know that I will need to declare this contribution in my self assessment so that I get the higher rate relief on it.

Does this mean HMRC will pay the higher rate relief directly to me in my bank account?

I.e. if i just arrange to pay extra into my pension via payroll, between my employer and their pension provider, everything is done automatically. I get the higher rate relief into my pension pot.

I'm wondering if I pay from after tax money, does this mean I can get my hands on more cash now?

I've got to be misunderstanding something. I suspect what I'm getting wrong is that any relief they do pay me, will probably count as income so if I'm trying to stick under £100k taxable income, this relief will put me over.