Perhaps it's best to let Richard Baxter (a key US delegate at the Geneva conference that led to the Geneva Conventions being concluded, and later judge at the International Court of Justice and generally regarded as one of the key authorities on the law of war) explain in his own words:

The great international lawyers of the past approached espionage, as they did so many other questions, from the standpoints of both law and morals. They were ultimately persuaded by the common view of mankind that persons acting as spies from patriotic motives pursue a moral course of conduct and concluded that the power of a belligerent to punish espionage directed against him arose not from the fact that the law prohibited the activity but from the danger which clandestine acts created and the resulting necessity that they be dealt with severely. How this view was to be reconciled with the safeguards generally accorded enemy soldiers is most persuasively stated in the words of Gentili: ‘This also is a reason why you should be unwilling to assume that role [of spy], because it is denied the privileges attaching to military service. And therefore the law against spies seems just, since they have divested themselves of the character which would prevent their being treated in that cruel and degrading fashion.’

(Source: Humanizing the Laws of War: Selected Writings of Richard Baxter (Vagts et al. ed., OUP 2013), 43)

Gentili was writing in the 16th century, as the Regius Professor at Civil Law at Oxford. It seems his view has carried over to the modern era; thus, at the conferences on the law of war that pre-date the Geneva Conventions, the status of spies was explicitly considered, but they were deliberately omitted from the scope of protections offered to combatants (save for having a right to trial): see art 19-22 on the Brussels Declaration of 1874 (ratified by 15 States) and the Hague Conventions of 1899 and 1907 (art 29-31). At the Hague conferences, Baxter cites the Belgian and Dutch delegations as being particularly hostile to further protections being accorded to spies.

This approach has been preserved in art 5 of Geneva Convention IV:

Where, in the territory of a Party to the conflict, the latter is satisfied that an individual protected person is definitely suspected of or engaged in activities hostile to the security of the State, such individual person shall not be entitled to claim such rights and privileges under the present Convention as would, if exercised in the favour of such individual person, be prejudicial to the security of such State.

Where in occupied territory an individual protected person is detained as a spy or saboteur, or as a person under definite suspicion of activity hostile to the security of the Occupying Power, such person shall, in those cases where absolute military security so requires, be regarded as having forfeited rights of communication under the present Convention.

In each case, such persons shall nevertheless be treated with humanity, and in case of trial, shall not be deprived of the rights of fair and regular trial prescribed by the present Convention. They shall also be granted the full rights and privileges of a protected person under the present Convention at the earliest date consistent with the security of the State or Occupying Power, as the case may be.

(See the ICRC website for further commentary on the background of this article).

At the time of the Geneva conferences it was the position in international law "that espionage is not in violation of the law of nations [i.e. international law] but that a belligerent [State] penalizes this conduct because of the danger it presents to [it]" (Baxter, 44), with few restrictions imposed by international law on what a State is entitled to do with respect to captured spies, which therefore falls to be governed by municipal law.

Baxter therefore writes (p. 46) that "an alien enemy engaging in espionage, although divesting himself of the protection he might otherwise enjoy as a prisoner of war, is in turn protected by the safeguards of domestic law, which... makes even active enemies benefit from the law’s protection". However, conducting a survey of the domestic laws applicable to spies might make one sceptical over whether this "benefit" is substantively meaningful -- the general tenor seems to be that captured spies are at the mercy of the enemy, a position that has remained consistent for many hundreds of years.

(Edit: formatting)

If you do not get an answer here, r/WarCollege might be able to assist