How long does an Activation Unlock with proof of purchase take?

Unless somebody happens by that has made such a request (and their answer may be exclusive to their particular case) then what we know is at:

How to remove Activation Lock - Apple Support

https://al-support.apple.com/#/additional-support

Note that Apple may be very particular about their proof of purchase. It appears to typically require the original bill of sale from Apple itself, or an Apple-authorized retailer. A third party reseller will likely be unacceptable.

We cannot tell you exactly, if you want to know more you might need to Contact - Official Apple Support For further support and assistance

Keep in mind that Activation Lock is an engineered, intentional theft-deterrent mechanism.

Anyone who claims that they are a legitimate owner who somehow “Activation-Locked” themselves out of their own device is understandably met with some skepticism.

Apple rightly requires quite compelling evidence of legitimate ownership — which must presumably be consistent with their own internal records — so as to avoid “handing over” a stolen device to a thief; and thereby becoming themselves complicit in the criminal activity.