I've learned that modal particles (doch, schon, ja, ...) usually have little meaning in terms of adding detail and information to a sentence. They tend to make sentences more lengthy without adding much (besides impact and emphasis). If so, would it be better to avoid using them in Academic writing?
It would indeed be better to avoid them in Academic writing, since it requires a different style of writing. It's supposed to be concise, impersonal and factual. Sentences should be as short, clear and to the point as possible.
Imagine a professor reading your final assignment. They also have many other things to do (among them maybe reading others' final assignments) and write a report about it. In order to assess it, they want a clear text containing the facts of your research or other project.
They are used to indicate how the speaker thinks that the content of the sentence relates to the participants' common knowledge or add mood to the meaning of the sentence.
and the German article adds
Sie dienen unter anderem dazu, die Einstellung eines Sprechers hinsichtlich der Satzaussage auszudrücken oder sie zu beurteilen.
In summary, they are not only an irrelevant addition, they are actually detrimental. The focus of your work is your work, not you and your opinion or feelings you want the reader to share. The place to add your assessment, but still in the formally correct form, is the Diskussion - but not before, so other's can form their own assessment without your guiding influence. There is no place to create a mood (you are not writing a novel). It's about facts, whether you uncovered them through research or created them (e. g. some project, maybe a program or a robot or whatever).
Avoid them as good as you can. If you feel you have to use them, take the time to reflect upon what you are trying to express and if you are maybe not in heading into a wrong direction. Then, change the approach. Reformulate it, because you can do without them, and without them, you are on the safe side.
Regarding the Diskussion, it's also still supposed to be impersonal. It's not a place to discuss how you feel about it, or the like.