If a person has a green card, they are required to file a US tax return and report and pay tax on all their world-wide income, even if they do not live or work in the US. This is one of the obligations placed on you for getting that green card. Regardless of how your spouse files, she can claim a credit or deduction on her US tax return if she pays tax to a foreign country on the same income, that will reduce the burden of double-taxation.
Your options are to each file as married filing separately, or file one joint return as married filing jointly. With married filing separately, you each list only your own specific income and deductions. MFS usually results in a higher tax bill, because some deductions and credits are reduced or disallowed, but it may have other advantages. With married filing jointly, you file one return listing all your combined income, deductions and credits. Whether you file MFS or MFJ, your spouse can claim the foreign tax credit.
Your real problem is with state taxes. Your wife is not a resident of CA (she is not domiciled there) even if you have the same address on her Visa application, because residency is determined by all the combined facts and circumstances. However, her income may be taxed in CA due to community property rules. @TomD8 may be able to help with filing in California.
Then lastly, your wife may be a dual-status alien for 2024. That means that her income from before the marriage is only taxed in her home country, unless it is considered "US source" income, and then all her income from after the marriage is taxed in the US. Dual-status is a situation that is not supported by Turbotax, and you might need professional assistance for the dual-status year (it gets easier when she has the green card for the whole year).
