If my wife made less than $10,000 last year, does she have to file taxes? Do I have to include her on my tax return?

You should be filing a joint return, and you include her income on the joint return.   ALL of your combined income goes on that one return.

If you were legally married at the end of 2023 your filing choices are married filing jointly or married filing separately.

Married Filing Jointly is usually better, even if one spouse had little or no income. When you file a joint return, you and your spouse will get the married filing jointly standard deduction of $27,700 (+$1500 for each spouse 65 or older)  You are eligible for more credits including education credits, earned income credit, child and dependent care credit, and a larger income limit to receive the child tax credit. 

If you choose to file married filing separately, both spouses have to file the same way—either you both itemize or you both use standard deduction. Your tax rate will be higher than on a joint return.

 Some of the special rules for filing separately include: you cannot get earned income credit, education credits, adoption credits, or deductions for student loan interest. A higher percent of your Social Security benefits may be taxable. Your limit for SALT (state and local taxes and sales tax) will be only $5000 per spouse. In many cases you will not be able to take the child and dependent care credit. The amount you can contribute to a retirement account will be affected. If you live in a community property state, you will be required to provide additional information regarding your spouse’s income. ( Community property states:  AZ, CA, ID, LA, NV, NM, TX, WA, WI)

 If  you are using online TurboTax to prepare your returns, you will need to prepare two separate returns and pay twice since with online, you get one return per fee.

https://ttlc.intuit.com/questions/1894449-married-filing-jointly-vs-married-filing-separately

https://ttlc.intuit.com/questions/1901162-married-filing-separately-in-community-property-states

https://ttlc.intuit.com/questions/1894449-is-it-better-for-a-married-couple-to-file-jointly-or-separately

If you were to file as married filing separately, and have no other unusual circumstances, your wife would not be required to file.  However, filing as married filing separately will significantly increase your taxes, because the tax rates are higher for MFS and many deductions and credits are reduced or disallowed.  The only way to know for sure is to test both ways.

If you file jointly, you must include all the income for both spouses, no matter how small a specific item might be.