Subject: Re: Biden releases 11 from Gitmo
The US Constitution does apply as soon as we take custody of them. The Constitution limits our government, and what it can do. It cannot detain someone indefinitely without trial, exercise cruel/unusual punishment, and other such things. The Constitution isn't concerned with "is it practical".

Not necessarily.
Prisoners of War are treated according to the Geneva Convention. Had they been designated as under the jurisdiction of a military tribunal then the law of the land with respect to them would have been the UCMJ (Uniform Code of Military Justice).