To address the military aspect, there are a few Byzantine military treatises which touch upon spying as an important component of military science. The first I will mention is by an unknown author, but it is thought to have been composed during the reign of Justinian, and our most complete copy comes from a part of codex Mediceo-Laurentianus graecus 55,4. It is a compilation copied at some point before 959, as it was done on the orders of Constantine VII Porphyrogenitus. George T. Dennis provides a translation in his Three Byzantine Military Treatises, and refers to it as "Anonymous Byzantine Treatise on Strategy." Pg.123-125 is a section specifically on spies and spying, mentioning details such as "spies must never be of the same race as the enemy," the spies family must reside in the empire and not in the lands of the enemy, and should not be someone that has "suffered any serious harm at our hands." It goes on:

They must, of course, be men of natural intelligence, well acquainted with the customs of the enemy to whom they are assigned, fluent in their language, and experienced travellers in their country.

Nothing earth shattering, but it gives an idea of some of the considerations taken when choosing a spy. Furthermore, the treatise provides an example of how a spy could get intelligence smuggled out, while maintaining their cover:

Before leaving on his assignment each spy should speak in secrecy about his mission to one of his closest associates. Both should agree upon arrangements for communicating safely with one another, setting a definite place and manner of meeting. The place could be the public market in which many of our people, as well as foreigners, gather. The manner could be on the pretext of trading. In this way they should be able to escape the notice of the enemy. One offers our goods for sale or barter, and the other gives foreign goods in exchange and informs us of the enemy's plans against us and of the situation in their country.

The treatise also provides some advice on what a spy should do when they arrive in the spied upon territory:

After arriving in hostile territory, they must not have any contact with prisoners of war, not only because it might arouse suspicion but also to avoid being recognized. In their constant association with the enemy they should steer clear of the baser sort and also of sharper and quick-witted men. They should, rather associate with people who are good, unsuspicious, and simple in their habits, and they may seek lodging with them.

Not quite a medieval 00VII, but like most of these treatises, the advice is very straightforward and to the point.

Other works on Byzantine Strategy cover intelligence gathering in passing such as the Taktika of Leo VI (also translated by George T. Dennis). In this one the references to intelligence gathering are a little more hands on, with a greater focus on scouts and scouting rather than specifically spies. It does though, speak of what a general should do when spies are discovered. On pg. 433, it is advised that if your force weaker than your opponent "kill the spies or hold them in a secure fortress." If on the other hand, your force is superior, let the spies observe the equipment, the numbers, the training, etc. and then "let them go so they can so inform their compatriots, who will then succumb to cowardice." Pg. 615-617 also talks about ways to root out spies in your own camp:

As a good hunter skillfully goes after wolves or catches foxes, so you should skillfully search out spies from the enemy. Station guards outside your campsite, then give the order for each man to take hold of the person next to him and not let him go until he tells him who his officer is and what tagma and squad he belongs to, or some other password. Subject those who are unable to name these to further questioning, and in this way you will uncover the spies.

This is a variant of what Vegetius advised half a century earlier (Vegetius: Epitome of Military Science, translated by N.P. Milner, pg. 118).

When an enemy spy is wandering secretly in camp, let all personnel be ordered to their tents in daylight, and the spy is immediately caught.

Maurice's Strategikon (yet another work translated by Dennis), also prefers the tent method, going into greater detail, but with the same ultimate result (pg. 105).

Each of these works also cover ways in how a general can minimize the information spies can gather from armies and movements. Some are simple suggestions, such as travel through uninhabited areas if possible, out of the sight-line of city walls. Other suggestions include when lining up for formation, to alter the depth and breadth of the units so it is more difficult for spies to judge the size of your armies. Advice that even the best spies find it difficult to accurately judge the size of armies greater than 20-30,000 men, etc. The list goes on. If you happen to be interested in other aspects of Byzantine military science, these sources are also a pretty good reading list.

tl;dr show me the sources:

George T. Dennis, Three Byzantine Military Treatises, Washington 2008.

George T. Dennis, The Taktika of Leo VI, Washington 2010.

George T. Dennis, Maurice's Strategikon, Philadelphia 1984.

N.P. Milner, Vegetius: Epitome of Military Science, Liverpool 2011.