The latter. I am 49.5 and depending on how things go have about 7 or 8 years of expenses in my taxable account and Roth contributions.
If you made the home purchase this year, then yes, I would imagine that TRP would send a notice of the withdrawal amount to the IRS. As you know there is an exemption for this, up to $10K I believe. I've never done that, but I think you'll report it on your taxes so it matches up with what the IRS is expecting.
And yes, if you take early withdrawals from your Roth, those will also be reported to the IRS by TRP, I believe on 1099-R. You'll provide the appropriate information to the IRS on Form 8606, Part III I think.
I'd recommend familiarizing yourself with Form 8606 and its instructions. I think the instructions are pretty confusing, but if you go slow and know what the law is you should be able to get it right. Also, there are examples out there on the web of Form 8606's filled out by people in our shoes, and those are helpful to understand where the numbers should go.