It's not a shared power.
The authority to declare war belongs to the legislative branch via Article 1, Section 8, Clause 11.
The ability to make peace belongs to the executive branch via Article 2, Section 2, Clause 2.
IMHO, the Founders rightly believed it should be difficult to start war, yet easy to end it.
§ 1168. In the convention, in the first draft of the constitution, the power was given merely "to make war." It was subsequently, and not without some struggle, altered to its present form. It was proposed to add the power "to make peace;" but this was unanimously rejected; upon the plain ground, that it more properly belonged to the treaty-making power. The experience of congress, under the confederation, of the difficulties, attendant upon vesting the treaty-making power in a large legislative body, was too deeply felt to justify the hazard of another experiment.
Joseph Story Commentaries on the Constitution
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Let's leave aside this was 25 years before. Do you know of anywhere the text of such pamphlets is available? I'm curious to read them.
No, but doing a general search for the year and the subject usually brings up something.
This is incomplete. The treaty-making power is shared with the Senate, which is required to "advise and consent" by a 2/3 majority to any treaty.
The "advise" portion has never really been implemented, but the consent portion still works. So the president cannot make peace without 2/3 of the Senate consenting. Though the Congress also does not really have the power to force the C in C to wage a war of which he disapproves.
The power to make war is also not exclusively legislative. Depending on what you define as "war," the US has been involved in some dozens of wars. The Congress has formally declared war only five times, most recently in 1941.
The control of the Congress over presidential war-making is much more related to the power of the purse than to the power to declare war, which we don't do anymore, though congressional authorizations to use force, as in the Iraq War, are IMO the functional equivalent.
As I said, the war and peace making powers are both shared between the legislative and executive.