"Isn't there something about being at war that is part of the crime of "treason"?"
No.
"The meaning of TREASON is the offense of attempting by overt acts to overthrow the government of the state to which the offender owes allegiance..."
https://www.merriam-webster.com/dictionary/treason
The office of the President is sworn to defend the Constitution, and this presumes upholding all the laws based on it, including defending the US border. Infiltrating hordes of foreign men to secret locations by flying them past the border designed to keep them out is giving aid and abetting foreign enemies of the United States to break it's laws, and the distinct likelihood that these foreign enemies are actually trained soldiers being concentrated in secret locations strongly suggests this is being done specifically to conquer and overthrow the USG.
"...the Congress would welcome said actions as part of the "continuity of government" credo."
Unless the above revolutionary intent is the actual reason, in which case the Senators and Representatives are likely to be removed with dispatch. It is this that most confounds me about this secret policy, because it's also likely that either willing puppets of the revolutionary junta or fresh blood recruited to replace the former elected officials, more likely both, will be necessary to take and hold power. Extant officials treacherous enough to serve a new regime might be expected to help the overthrow, but there are also likely to be more that will be lined up against walls and shot.
Such overthrows are notoriously dicey, and I suspect the lack of clamor over this policy is due more to it's secrecy than to ubiquitous participation by elected officials.
"It's far beyond time for anyone to plausibly believe that the government - of ANY country, but especially of the USA and its allies - are not at war with those not in government."
You are absolutely correct.
Thanks!