If you gave the forwarding form to the post office any mailed forms should go to your new address. You could also inform any employer of your new address.
with the IRS file form 8822. normally the refund is sent to the address on the return. then if you have given the USPS a change of address notice it should be forwarded but this could take some time. if the IRS gets and processes the 8822 before the refund is issued it should be sent to the address on the form.
If you are talking about the 2022 W-2's or 1099's that will be sent out in January or early February 2023 for your 2022 tax return, you have plenty of time to notify your past employers and anyone else that you have a change of address. And of course you need to change your address with the US post office so that your mail will be forwarded to your new address. You can use a change of address form to tell the IRS that you moved----or when you file your 2022 tax return, make sure you use your current mailing address on the tax form.
https://www.irs.gov/faqs/irs-procedures/address-changes/address-changes