This is a very interesting question and I will try to answer it for you. There are two ways to look at it, both with it's pros and cons. I understand the question as follows: "what did the general people, the everyday man or woman, of the Holy Roman Empire think?". Another way to look at it would be: "what did the warring parties leaders (the emperor, the kings of France/Sweden/Denmark, the countless princes of the Holy Roman Empire) think of those wars, one big one or multiple shorter ones?" I'll be answering the first and give a quick view on the second later.

To make it quick short and simple: the people of the HRE viewed the Thirty Years War as one big war that was at large one thing. As always, there are questions to be asked here but also - more on that later.

As a groundstone for my answer I will take into consideration 3 eye witness reports that are in my opinion vicarious for the general populus of the HRE. There is on one hand the farmer and shoemaker "Hans Heberle" that wrote a form of diary the "Zeytregister" (timeline of what happened). He, in this, writes about his experiences and the influence the war had on him, living in a village close to Ulm in 'South-Germany'. What is of importance in this is the fact, that he never talks about the wars as different and while he does talk about the war "reaching Germany" in the early 1620s (telling us that Bohemia wasn't necessarily viewed as German by contemporaries) he never talks about different wars but views it as one entire war complex. How the Swedish land at the Baltic Sea coast isn't "a new war" it is viewed as a saving from the heretic Catholics (Heberle was a lutheran protestant). He also speaks about the different peace treaties' but not as in them ending a war, but rather as an armistice. They are stopping the fighting, but it doesn't appear to be peace for him. Until the Westphalian Treaties. This is where Heberle finally "celebrates peace". He talks at length about the festivities and how it now finally appears to be over. Taking these things into consideration this war appears to be one whole one, with different phases of war and no war.

Then there is the diary of the mercenary Peter Hagendorf. He also wrote about his experiences during the Thirty Years War (he is also a very interesting starting point to ask the question of 'was this a war about religion or not? To whom was or wasn't it one?' - as is Heberle). In my opinion his writing isn't as important or clear when it comes to answering your question but it still tells us one thing: being a mercenary was a way of life. The mercenaries were dependant on the war and his diary talks about the life 'on the road' and how it was to live and die in the 'Tross' (a kind of appendix to the moving army filled with physicians, traders, fencers, cooks, prostitutes, the families of the mercenaries, etc.). One thing that he talks about at the end of the Thirty Years War is the fact that he now is lost, there is no more war to fight and since all he knows is being a mercenary he does not know what to do anymore. He drinks, his writing becomes partially unreadable and slightly incoherent, telling us that he was somehow lost. But he does call the Thirty Years War "the last war" and means all his time spent in the armies he fought in. Not the last part of the Thirty Years War, all of it.

The last person I want to talk about is Andreas Gryphius. He presents (in my opinion) one of the strongest argument for a "the Thirty Years War was viewed as one continuous war". In his sonnett "Tränen des Vaterlandes" ('tears of the fatherland') from 1636 he writes in verse 10 "Dreimal sind schon sechs Jahr, als unser Ströme Flut". The important part here is the one before the comma. 'three times six years already,...'. So in 1636 he made 1618 out as the date to the beginning of all the warring and bloodshed in the HRE. Since this sonnett is in general talking about the war and it's atrocities, it is a strong point to make that he, in 1636, where we arguably are already in the fourth phase of the war, with different peace treaties in place in between the phases, was looking at the fighting and thinking of it as connected, as one big war.

Now, the question is "how significant are three people's views, when we think about this question?". Well, here we kind of have to fall back to Ockham's Razor and general believability of source material. First of all, there is no reason to assume those sources would be lying about this question, so we are good on that front. Second of all, they are in my opinion giving us good reason to assume that they viewed the warring as connected and not different wars, while never actively stating the opposite. This leads us to third the crux of history - we will never know "for sure" but I do believe there is good reason to assume that the Thirty Years War was viewed as one war by contemporaries. As long as the opposite cannot be said with the same level of certainty I am leaning to what I have tried to lay out above.

Lastly I want to give you a quick look into the second question I opened up (what did the warring parties leaders think of those wars, one big one or multiple shorter ones?). Here I would also intuitively lean towards "yes, one continuous war", but I am not able to provide the same source material. Why I lean this way is mainly influenced by how I would interpretate the Westphalian Peace Treaty. It is at large a treaty that took years to formulate and also one that comments and relies heavily on the "Augsburger Religionsfrieden". Due to this I think it is reasonable to assume that treaties up until then were viewed as temporary solutions, especially when you take into consideration that all the phases relied onto what happened before. The second phase wouldn't have happened without the first, etc. This is true for all of them and the arguments that are made to continue the fighting are always coming as a response to the previous fighting. This is quite the weak argument in comparison to what I said about the first question so I hope someone else can back me up with source material here as well.

If you want to further read into the war itself I will name a few works that will give you an overview of the war itself and the scientific discussion around it:

BURKHARDT, Johannes: Der Dreißigjährige Krieg, Berlin 1992. BURKHARDT, Johannes: Der Krieg der Kriege, Stuttgart 2018.

GOTTHARD, Axel: Der Dreißigjährige Krieg, Cologne/Weimar/Vienna 2016.

JESSEN, Hans: Der Dreissigjährige Krieg in Augenzeugenberichten, Düsseldorf 1963.

MÜNKLER, Herfried: Der Dreissigjährige Krieg, Berlin 2017.

SCHMIDT, Georg: Die Reiter der Apokalypse, Munich 2018.

These are all in German, you may be able to find some of them translated but I am not sure, sorry! For English sources I can recommend:

PARKER, Geoffry: The Thirty Years' War, London 1997 (this is the second or third print, not the original though, that is from the late 1970s).

WILSON, Peter H.: The Thirty Years War, London 2009.

As source material I have used (I don't have the entire citation with me right now, should you want it, just tell me and I'll add them!):

GRYPHIUS, Andreas: Tränen des Vaterlandes.

HAGENDORF, Peter: Tagebuch eines Söldners.

HEBERLE, Hans: Zeytregister.

I am sorry for the formatting, I am writing this on my phone and am not good at it, but I hope this answers your question.