Generally you should have provided a document about your status to the bank, and should have changed it with the change of status. As a non-resident that would be a W8-BEN, as a resident that would be W9.
However, it is not surprising that a foreigner new to the US knows nothing of this nonsense, so you’re not alone or in any unique position.
To report the income you don’t really need neither 1042-S nor 1099, you just report it as appropriate. Usually the sign-up bonuses are considered interest and would be reported together with all the other interest on your Schedule B.
If there were any taxes withheld, it should be shown on your 1042-S line 10. That should flow to your form 1040 line 25c.
See the instructions for the form 1040 that cover this case:
Also include on line 25c any tax withheld that is shown on Form 1042-S, Form 8805, or Form 8288-A. To assist in processing, attach the form to your return to claim a credit for the withholding.
You’ll need to check with the Sprintax support how that should happen and what screens you need to use and what fields to fill.
Provide an updated W9 to your bank to avoid this happening again in the future.
