He is subject to the Constitution at all times, which gives Congress the authority to declare war (Article 1 Section 8 Clause 11), which would define being in “war-time”, not the President.
The Constitution defines treason, and is the only place in the Constitution in which the standards for Conviction are put forth in the Constitution itself (Article 3 Section 3), which consists of being convicted in a court, not at the whim of the President neither in time of peace or time of war.
Article 1 Section 8 Clause 4 gives the authority to make rules on naturalization and citizenship, and the loss thereof, which is congruent with Article 3 Section 3, and such rules must be followed by the President in both times of peace and times of war.
Even the power to suspend Habeas Corpus is given solely to Congress in Article 1 Section 9 Clause 2 either in times of war or times of peace, and not to the President.
The President, whether in war or peace, shall have Power, by and with the Advice and Consent of the Senate, to make Treaties, provided two thirds of the Senators present concur (Article 2 Section 2)
He is charged to “take Care that the Laws be faithfully executed” (laws which the Legislative branch [Congress] writes in accordance with the Constitution) (Article 2 Section 3) after taking an oath to “preserve, protect and defend the Constitution of the United States” (Article 2 Section 1).
You should rethink your erroneous position that there are no qualifications or limitations to the President’s authority in either war or peace, which remains unsupported.