The examples given by you can be ascribed to the religion, because they fall under its general principles. So we can say, "Preserving the Qur'an is from Islam, the Shariah" and "laying down the usul of tafseer, or fiqh, or ilm al-hadith is from the Shariah", as these matters have their principles rooted in the Shariah (in the case of these examples), or they are indicated by its general principles. To exclude these matters from wrongly being put under the ihdaath (inventing, introducing) which is rejected, a qualification has to be made to exclude what would fall under "general" Shariah proofs or principles, such as "
that without which an obligation cannot be fulfilled is itself an obligation" and so on. So these things aid the religion (as you said), but they
have a basis in the religion (Shariah texts) as well, through general principles, and this is part and parcel of the Shariah's universality for all times and places, and we believe that all beneficial interests are already included in broad Shariah principles, and hence we can say that they are from and indicated by the Shariah. This is whilst we keep in mind that this definition is aimed at
excluding everything that is not an innovation, and including only what is an innovation in the Shariah sense. So this why it is said "
that which is innovated and does not have a general or a specific proof from the Shariah."
But if we were
defining what is from the Sunnah only (excluding everything which is bidah in the religion), then we would have a different definition, in this case "
That which must have a specific proof in the Shariah [for both its foundations (e.g. prayer) and its details (i.e. praying in specific way at specific time tied to specific cause, such as eclipse prayer, funeral prayer)]. Here we have a specific proof for all elements of an act of worship, and innovation can't be included here and neither can maslahah mursalah, because that only has a "general proof" - for example, there is no specific proof in the Shariah which says to put the Qur'an into a single book, only a general principle under which it comes, and likewise, no
specific proof to formally and systematically lay down the usul of fiqh, or to build a hospital or a school, or to define the rules of ilm al-hadith. All of these are simply wasaa'il (ways and means) which are supported by general Shariah principles because through them, Shariah goals are facilitated. This is unlike all matters of worship, they all have explicit specific proofs for their foundations (e.g. fasting in and of itself, or prayer) and their details and characteristics (when, how, conditions etc.), and innovation therein is strictly prohibited, since the deen in that regard is perfected and completed, there being nothing which brings closer to Paradise, except that it has been explained by the Messenger (
as per the hadeeths in this regard).
There is a subtle difference, but I hope you can see it from the example given. Refer to al-Shatibi's I'tisaam and some of the resources listed in the articles for more clarification.