I fell for a scam, logged into their account under the pretext of an app, and now they're demanding a ransom.

Bummer.

The only way out of this is to take the phone and the proof of purchase from Apple or an authorized retailer to Apple to have the activation lock removed.

If you can't provide proof that you are the original purchaser, it's a brick. There is no way to bypass the activation lock.

You will need the original purchase receipt.

Go here and read:

How to remove Activation Lock - Apple Support

EvonWee wrote:

I have a receipt for the purchase, but there is a catch, I resident of Russia.

Then there is NOTHING anyone here or at Apple can do for you. Apple has no support in Russia. That was a most unfortunate thing you did. NEVER sign into someone else's account on your phone. You have turned the phone over to them and paying them the ransom would also be most unwise. Once they get it that you're willing to pay, they'll demand more.

EvonWee wrote:

Will it help if I reset my phone to factory settings at the service center?

No.

Think about it. If thieves could get past Activation Lock simply by resetting a phone, it wouldn't be very useful. Activation Lock exists in no small part to prevent thieves from successfully resetting a phone!

In this case, the scammers have turned Activation Lock on you. It is much as if you gave scammers your house key, then came home to find that the scammers had changed the deadbolt locks on all of your doors while you were out, so that you could no longer get into your own home.

EvonWee wrote:

Will it help if I reset my phone to factory settings at the service center?

No. You won't be able to reset the phone. If you could have and it was that simple, you'd have already done so. Face it. You allowed yourself to be scammed and there is nothing you, us or Apple can do for you.

Sorry, there is nothing you will be able to do. It is a tough lesson to learn, but trusting anonymous users on the internet by entering their credentials into your phone is always going to result in a poor outcome.

Bummer. As you're probably aware, no support is available in Russia at this time. Apple has suspended all business operations there as Russia is under international sanctions.