I am a US citizen residing abroad. I file my U.S. federal income tax return every year using my permanent foreign address. I just received a letter from my U.S. bank along with a Form W-8 BEN. Does this form apply to me

No, Form W-8 BEN does not apply to you. Since you are a U.S. citizen, regardless of where you live, you should provide your U.S. bank or payer with a completed Form W-9, Request for Taxpayer Identification Number and Certification. This form is used to:

1. Certify that the tax identification number you are giving is correct (or you are waiting for a number to be issued),
2. Certify that you are not subject to backup withholding, or
3. Claim exemption from backup withholding applicable to payees that do not provide a valid TIN or are U.S. exempt payees.

Form W-8 BEN is generally used by foreign persons to establish that they are not U.S. persons, to claim that they are the beneficial owner of the income for which Form W-8 BEN is being provided, and, if applicable, to claim a reduced rate of, or exemption from, withholding as a resident of a foreign country with which the United States has an income tax treaty. Since you are a U.S. citizen, you should use Form W-9 instead.

Sources:
Publication 519 (2023)
Publication 54 (2023)
IRM Part 21. Customer Account Services. Chapter 8. International. Section 2. BMF International Adjustments
Publication 1281 (12/2023)
IRM Part 4. Examining Process. Chapter 10. Examination of Returns. Section 21. U.S. Withholding Agent Examinations - Form 1042