Is it legal to charge credit card debt in full from the payroll account of the same bank?

Yes. When you sign up for a bank's product (e.g., a savings account), one of the documents that the bank requires you to sign is the terms and conditions governing the use of said product. These terms and conditions usually provide that in case the bank's client has a liability to the bank (e.g., unpaid credit card debt), the bank is authorized to set-off any amount due and owing to the bank against the account/s maintained by the client with the same bank.

This happens more often than people think, and banks usually justify this by something called right of set off. But the bank cannot just abuse this right, especially if it wipes out your entire salary and leaves you with nothing to live on.
Let me explain this clearly and what you can do immediately.
Firstly, the legal concept. Banks rely on compensation or set off under the Civil Code, meaning if you owe the bank and you also have money deposited with them, they offset the amounts. But this is not unlimited, and it can be questioned if it becomes abusive or unconscionable.
Secondly, salary is somewhat protected. Your payroll account contains wages, and under the Labor Code and jurisprudence, wages are given protection because they are for basic living. If the bank takes everything and leaves the account negative, that can be argued as abuse of rights under Article 19 of the Civil Code.
Thirdly, what you should do now, practical steps.
1.) Immediately open a new payroll account in a different bank. Tell your employer to transfer your payroll there starting this cutoff. Do not let the same bank receive your salary again or it will keep auto deducting.
2.) Write the bank immediately. Go to the branch and submit a letter requesting: Stop automatic set off on your payroll account; Restructure the credit card instead; Return at least a portion of the salary taken because it is for living expenses
Use the words financial hardship and request for restructuring. Banks respond better to restructuring than to confrontation.
3.) File a complaint with BSP if the bank refuses. You can file online at Bangko Sentral Consumer Affairs. The argument is: bank took entire salary; Caused negative balance; Left depositor without means for basic necessities; This becomes unfair or abusive banking practice.
4.) Negotiate, not fight immediately. From experience, the bank will usually offer: Installment program; Lower interest; Waiver of penalties; Return of partial amount taken
But you must talk to their collections or restructuring department, not just the branch teller.
Very important practical advice. Do not let your salary enter that bank again until this is resolved. Because legally, once the money is in the bank, they will set it off again.
If you want, I can draft a letter to the bank requesting restructuring and partial refund of the deducted salary. That usually works faster than verbal requests.