Midway through 2023 I was promoted from a nonexempt position to an exempt position. Because it all occurred within the same company I'm unsure how I would go about filing my taxes to reflect this change in filing status. And just to note taxes are still being taken out of my paychecks, so I'm unsure if that will also have an affect on this...
there is no impact on your filing status. it remains the same.
You will get a W-2 at the end of the year that reports all your wages and tax withholding. Your status as hourly, exempt, non-exempt, etc. has no effect on your tax situation with the IRS—the IRS taxes your income and it doesn't matter how you earn it.
When you were hired, you filed a W-4. That is used by your employer to estimate the amount of taxes to withhold from your paycheck so that you mostly break even at the end of the year. You might owe a small amount or get a modest refund but you should not owe more than $1000 and you should not get a huge refund. The formula used by the employer to calculate your withholding is self-adjusting; the more you earn, the more tax is withheld, so your withholding should keep up with your raise automatically. You would only need to file a new W-4 if you got a second job at the same time as the first, got married, or had a child, or certain other major life events.