When you prepare your next tax return, you will use your current address on the return. Information flows from your federal return to your state return, so both returns should display your current address. You can also send in a change of address form to the IRS if you want to.
https://www.irs.gov/faqs/irs-procedures/address-changes/address-changes
As for changing your address with the state--- since we do not know what state you are in, you will need to look up how to contact your state.
When you say you "recently" moved to another state---there are some other concerns. If you lived and/or worked in one state during part of 2025 and have now moved to another state and are working in that new state, you might need to prepare and file part-year returns for each of those states for 2025, depending on what states are involved. You have not mentioned the states. Several states have no state income tax; several states have reciprocal agreements with each other, etc. etc.
MOVED OR NEED TO FILE PART-YEAR STATE
https://ttlc.intuit.com/questions/1901560-how-do-i-file-if-i-moved-to-a-different-state-last-year
ALLOCATE PART YEAR
Use form 8822 to change address for the IRS. Contact your state taxing agency to change that one.
https://www.irs.gov/pub/irs-pdf/f8822.pdf