Vegetius’s De re militari seems to be somewhat on point, and though in a brief skim and search I couldn’t find specific instruction to lean into an attack, this was interesting:

THE POST EXERCISE

We are informed by the writings of the ancients that, among their other exercises, they had that of the post. They gave their recruits round bucklers woven with willows, twice as heavy as those used on real service, and wooden swords double the weight of the common ones. They exercised them with these at the post both morning and afternoon.

This is an invention of the greatest use, not only to soldiers, but also to gladiators. No man of either profession ever distinguished himself in the circus or field of battle, who was not perfect in this kind of exercise. Every soldier, therefore, fixed a post firmly in the ground, about the height of six feet. Against this, as against a real enemy, the recruit was exercised with the above mentioned arms, as it were with the common shield and sword, sometimes aiming At the head or face, sometimes at the sides, at others endeavoring to strike at the thighs or legs. He was instructed in what manner to advance and retire, and in short how to take every advantage of his adversary; but was thus above all particularly cautioned not to lay himself open to his antagonist while aiming his stroke at him.

NOT TO CUT, BUT TO THRUST WITH THE SWORD

They were likewise taught not to cut but to thrust with their swords. For the Romans not only made a jest of those who fought with the edge of that weapon, but always found them an easy conquest. A stroke with the edges, though made with ever so much force, seldom kills, as the vital parts of the body are defended both by the bones and armor. On the contrary, a stab, though it penetrates but two inches, is generally fatal. Besides in the attitude of striking, it is impossible to avoid exposing the right arm and side; but on the other hand, the body is covered while a thrust is given, and the adversary receives the point before he sees the sword. This was the method of fighting principally used by the Romans, and their reason for exercising recruits with arms of such a weight at first was, that when they came to carry the common ones so much lighter, the greater difference might enable them to act with greater security and alacrity in time of action.