Assuming you were under contract on the house prior to December 16, 2017 and closed prior to April 1, 2018, you are grandfathered in to the $1M limit, so no impact to you unless you're married filing separately.
Since you live there, you cannot claim rental losses (even if you didn't live there, likely no benefit due to AGI, unless you're a real estate professional). You will offset rental income by a percentage of the expenses you listed in addition to depreciation of the rented portion and other expenses like maintenance/repairs. The percentage used is based on how much of the unit is rented. Count 2/3 of any common rooms as rented, and all of any rooms exclusive to tenants as rented. It's acceptable to use room count or square footage in this calculation, likely you'll want to use square footage unless you have a lot of rooms that are exclusive to you (because your rent income is well below rental expenses, you want to minimize rented portion).
If we assume 2/3 is rented, you can use 1/3 of property tax and mortgage interest as itemized deductions.
Using your example numbers you'd have $20,000 in itemized deductions.
On the rental side 2/3 of each expense, so:
- Mortgage interest = $2,666
- HOA = $400
- Property tax = $666
- Depreciation = $2020
That's $5,752 in monthly rental expenses (plus maintenance/repairs, insurance, etc.), which fully offsets $3,000/month in rental income leaving you with no tax obligation on the rental side. However, when you sell you will face unrecaptured section 1250 gain even though you're getting no benefit from depreciating the rental portion of your property.
Using whichever method of calculating rented portion that results in a lower percentage would be beneficial to you.