It depends!! This is a gray area that the IRS hasn't specifically addressed. In reading this FAQ sheet from the IRS, under the heading of Who Needs to Report, it says "A U.S. person is a citizen or resident of the United States or any domestic legal entity such as a partnership, corporation, limited liability company, estate or trust". Your wife does not fit any of these parameters, even if she obtains an ITIN.
If you have signing authority on her accounts however, then you would need to file an FBAR from the time you were granted signing ability. If were granted signing ability in 2022 or 2023, you would need to file an amended FBAR for those years.
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