I am assuming that this isn't a rental property.
Is there likely to be any issue with getting flagged by the IRS
because they already have the 1098 from the mortgage lender but I
don't have it reported in what I filed in my 1040?
If you took the standard deduction, then the mortgage interest doesn't impact you federal taxes. The IRS won't be looking for it because you didn't need it.
Of course if adding in the numbers for your mortgage interest would put you over the standard deduction then you also want to change via the 1040x from the standard deduction to itemizing.
if you were already itemizing then the mortgage interest numbers would be very important to be able to claim all your deductions., and I would have expected to see your taxes change.
It is also possible that if you bought this house late in the year that the amount of interest wasn't enough to take you above the standard deduction. But next year you will have 12 months of interest so you need to make sure you include the 2022 1098 in your taxes.
If this is a rental property, then you will want to include the 1098, because you always want to include that cost in your tax calculation
Note: the IRS will never require you to include your mortgage interest 1098 for your personal residence if you don't want to itemize. That is always up to you.