Short Answer:
The duchies and prinicpalities in Silesia became part of the Holy Roman Empire whenever their dukes and princes became directly subordinated to the Emperor of the Romans, or whenever those dukes and princes were subordinated to someone who was suboradinate to the Emperor. So the principalities in Silesia were part of the Holy Roman Empire whenever there rulers were directly or indirectlysubordinate to the Emperor of the Romans.
Long Answer:
Originally - more or less - the duchies and principalities in the region of Silesia were part of Poland, though Bohemia and Poland fought over possession of Silesia and other lands soemetimes.
When Silesia was part of Poland, any dukes or princes rulingpart of Silesia would be vassals or otherwise subordinate to the ruler of all Poland, whether that ruler was a king or a senior duke.
Remember than the Emperor of the Romans in the Holy Roman Empire had many diferent layers of political power.
YOu might say that his strongest degree of power was in the lands that he owned and was the lord of.
And the next strongest degree of power might be said to be in the counties -if any -he happened to be the count of and thus had some authority over the lords in those counties.
And the third strongest degree of pwoer might be said to be in the duchies - if any - he happened to be the duke of and thus had some authority over the lords in counts in those duchies.
And the fourth strongest degree of power might be said to be in the kingdomss - if any - he happeend to be the king of and thus had some authority over the lords, counts, and dukes in.
So far, the same might said about any feudal ruler. A cound a was usually more m powerful than anyone lord in his country, because he authority over many lordships, but he had more power over a lordship which he owned than over a lordship which he didn't own and whose lord was his vassel.
Similarly a Duke had more power in the counties and lordships he owned than in the counties and lordships in his duchy he didn't own, but he had power than any one lord or count in the duchy, because he had overlordship over all the duchy.
Similarly a king had more power in the duchies and counties and lordships he owned than in the duchies and counties and lordships in his kingdom he didn't own, but he had more power than any one lord or count or duke in the kingdom, because he had overlordship over all the kingdom.
From 962 the offices and positions of King of the East Franks or of Germany, and King of the Lombards or of Italy or Lombardy, were united with the office and position of Emperor. And from 1032 the position of KIng of Arles or Burgundy was united with the position of Emperor.
Disregarding possible problems with defining the borders of medieval kingdoms, after 1032, if someone knew that a place was within the borders of any one of the three kingdoms of Germany, Lombardy, or Burgundy, they would know that it was within the Holy Roman Empire.
But knowing that a place was outside of one of those kingdoms wasn't enough to prove that was outside of of the Holy Roman Empire as a whole.
The Emperor was the overlord of places which were not inside his three kingdoms, just as within one of his kingdoms he was the overlord of places which were not within any duchy or country he was the duke or count of.
Bohemia became a duchy whose duke was more or less subordiante to the king of Germany, and then in 962 the duke became subordinate to the Emperor. Was the Duchy of Bohemia part of the Kingdom of Germany before 962, or was it outside of the Kingdom of Germany before 962, but subordinae to it? I don't know. If the Duchy of Bohemia was part of the Kingdom of Germany before 962, was it part of the KiIngdom of Germany which was part of the Holy Roman Empire after 962, or was it now independent of the Kingdom of Germany and part of the Holy Roman Empire? I don't know.
After one or two dukes of Bohemia who were appointe dlife kings of Bohemia, Bohemia became a permanent kingdom in 1212. And you might say that Bohemia became independent of the Kingdom Germany and directly dependent on the Empire in 1212, even if that wasn't already the case. Because a kngdom can't be part of another kingdom, right?
From 1745 to 1867 a state called the Kingdom of Slavonia existed which was more or less part of a state called the kingdom of Coratia,which was more or less a part of a state called the kingdom of Hungary. So that is an example of a kingdom within a kingdom within a Kingdom in modern Eruope.
So I don't whether Bohemia which was part of the HOly Roman Empire for about 844 years, was always part of the Kingdom of Germany, never a part of the Kingdom of Germany, originally part of the Kingdom of Germany but later outside of the Kingdom of Germany.
Anyway, most people who haven't considered the matter as carefully as I have, and so aren't as confused as I am, would use Bohemia as an example of a place which was not part of the Emperor's three kingdoms but which was part of the Holy Roman Empire.
Anyway, the emperors did have overlordship over lands outside the three kingdoms which belong to the emperor. For example, in the first three centuries or so of the HOly Roman Empire, it was common for the emperor to be the overlord of Hungary, Poland, and Denmark as well as Bohemia.
And the ideology of the Roman Empire was that the Roman Gods had granted to the Romans the right and duty to conquer the world and bring peace and order to it. The Romans didn't claim that they had the the right to rule the lands they conquered, but instead they claimed they conquered the lands they conquered because they already had the divinely granted right to rule the world.
And that became the political ideology of Christians in the later Roman Empire, except that they substituted the Christian God for the pagan Roman gods as the diviinity granting the right to rule. According to that ideology the Roman Emperor was the rightful ruler of the world.
So there were people all over what could be called Latin using Christiandom, or Roman Catholic Christiandom, who consideed the emperor of the Holy Roman Empire to be not an emperor, but THE EMPEROR, the rightful ruler of the world. From Spain and Portugal in the southwest to the lands of the Teutonic KNights and Finland in the Northeast, From northernmost Norway to Southernmost sicily, from Croatia and Hungary in the southeast to Ireland and Iceland in the northwest, There were peoplewho considerd the Emper of the HOly Roman Empire the emperor of the world and all the world part of the Holy Roman Empire.
Thus it is possible to claim that Silesia was always part of the Holy Roman Empire since Silesia was always part of the world.
And when Silesia was a part of Poland, Silesia was part of the Holy Roman Empire whenever the senior duke or the king of Poland was subordinate to the emperor.
And when the kings of Bohemia made the dukes and princes in Silesia their vassals instead of vassals of the Ruler of Poland, Silesia became part of the HOly RomanEmpire - ifit was not aleady part of the Holy Roman Empire - because the king of Bohemia was a vassal of the Emperor and Bohemia was part of the Empire.
As for maps showing Silesia as part of the Holy Roman Empire during the era of theHOhenstaufen, I think thatthey are probably in error if they don't show all of Poland also part of the Empire.
I might be wrong, and there might be some reason I haven't heard of why Silesia was more a part of the Holy Roman in that era than other parts of Poland. But as far as I know Silesia was no more or less a part of the Holy Roman Empire than any other part of Poland in the Hohenstaufen era.
So in my opinion maps of that era should either show all of Poland including Silesia outside of the HOly Roman Empire or all of Poland including Silesia inside the Holy Roman Empire, which I prefere. It seems wrong to me to depict Silesia inside the Holy Roman Empire and the rest of Poland outside the Holy Roman Empire in that era.