It's interesting because these "classic" writings mainly come from Wu Yuxiang, who studied with Yang Luchang and also Chen Qingping (Zhaobao style). Hao learned from Wu style, and Sun Lutang learned from Hao style. The writings then influence people from all styles, but we could say Wu is kind of the connection to Chen, Yang, Wu, Hao, and Sun. They are all pretty consistent in what they say when you read Hao and Sun. For example (I'm adding the emphasis):
TAIJI BOXING’S SOLO SET & PLAYING HANDS (by Hao Yueru)
太極拳不在樣式而在氣勢,不在外面而在內。平日行功走架,須研究揣摩空鬆圓活之道,要神氣鼓蕩,全身好似氣球,氣勢貴騰挪,身體有如懸空。兩手無論高低屈伸,一前一後,一左一右,皆能靈活自如。兩腿不論前進後退,左右旋轉,虛實變換,無不隨意所欲。日久功深,有不知手之舞之,足之蹈之之境。明白原理,練熟身法,善於用意,巧於運氣,到此地步,一舉一動,皆能合度,無所謂不對。
[Section 1]
Taiji Boxing lies not in the postures, but in the energy, not on the outside, but on the inside. When practicing the solo set, it is necessary to study and contemplate the methods of emptiness, relaxation, roundness, and liveliness. Your spirit and energy should be activated, your whole body seem like a balloon, energy should be ready to move, and your body seem suspended from above. Your hands, regardless of being high or low, withdrawn or extended, one forward while the other is back, or one to the left while the other is to the right, should always be able to move nimbly and smoothly. Your legs, regardless of advancing or retreating, turning to either side, or alternating between empty and full, should always follow your mind’s wishes.
Over time your skill will deepen and there will be the condition of being unaware of the movements of your hands and feet. Understand the principles, become well-versed in the body standards, perfect the use of intention, and become skillful at moving energy – when this condition is achieved, every movement can be done to the proper degree, and there will not be a moment in which anything is incorrect.
Essentially he gives a characterization of the art itself. His characterization is essentially the same as Wu's and Sun's writings. Notice how much they all talk about sinking and moving energy (and elsewhere) and being able to do this until it's an unconscious ability. They almost always mention this advice at the very beginning of their writing. For some reason, people quite literally ignore all of this. Here is what Sun says about taiji before he goes into postures, feet/waist, etc., etc.:
Once conceived, a person is imbued with a nourishing primordial energy, which does not veer in any direction from its function, for it is balanced and does not leak away. It is perfect and complete. It is genuine active energy, so it is considered an energy of centered harmoniousness. This energy tends to fill the limbs and bones, no place where it is not there, no moment when it is not so, both internally and externally, flowing unceasingly.
Consequently the expanding and contracting, movement and stillness of this art come from this energy. The marvels of releasing and extending, gathering and shrinking, come from this energy. Expanding is [releasing,] extending, and movement. Contracting is gathering, shrinking, and stillness. Expanding is active. Contracting is passive. Releasing, extending, and movement are active. Gathering, shrinking, and stillness are passive. Expanding and contracting are a continuous movement of passive and active, a taiji continuousness.