There are two pieces of evidence I found as to why the words Ar-Rahman and Ar-Raheem are interpreted the way you mentioned. The first is the word etymology itself, and the second is the linguistic use of both words.
Both Ar-Rahman and Ar-Raheem mean the one who has a lot of mercy.
Ar-Rahman comes in the pattern of "فَعْلَان" and this pattern is only said when you want to emphasize something greatly. For example, "غَضْبَان" (a form of "angry") is used for someone who is completely overcome and covered with anger. "عَطْشَان" (a form of "thirsty") is used when someone is completely overcome by thirst.
This form of word is always to emphasize the meaning. That is why Ar-Rahman is said to mean when someone's mercy completely covers everything. However, this form also implies temporariness. Obviously, no one remains extremely angry forever and likewise with extreme thirst.
Allah says in the Quran:
وَرَحْمَتِي وَسِعَتْ كُلَّ شَيْءٍ
[...] My mercy encompasses all things [...] (7:156)
That is why Ar-Rahman is for everyone, Muslim or Kafir, good or bad. Ar-Rahman is the one who created everyone and blesses everyone on Earth regardless of their religion with food, water, and everything for them to live.
The word form of Raheem follows the pattern of "فَعِيل." This is also a form of emphasis of the action (in this case of mercy), however "فَعِيل" is weaker than the previous form. It is also said to be weaker because it can be used both as the actor and the object of the action (i.e. Raheem can also be used sometimes as a word for the one upon whom mercy had come).
This means this form is not as strong as the previous one which can only ever be used for emphasizing the action of the actor. This form also implies a quality that is more permanent.
Regarding the linguistic usage of the two words, Rahman is not used except for God however Raheem (which means someone who has a lot of mercy) is used for other people (for example Prophet is described as merciful using Raheem in 9:128).
The reason Rahman is not used for other people is that no one other than Allah has the ability, motivation, or power to be merciful and giving in the extreme amount Allah can or to the amount of people Allah can. As humans, we only have the ability to be merciful to specific people or groups in limited amounts.
That is why Raheem is said to be specific in action towards a group because it is a word other people than Allah can also be described with. However, note that Raheem is still emphasized in meaning; it is simply not as emphasized as Rahman.
With those evidences, we have concluded that Rahman is more expansive and intensive in meaning than Raheem. But, Raheem is a more permanent and consistent in meaning.
At this point, you could point out verses in the Quran to decide what exactly the difference of one from the other is about.
For example, Allah usually uses Raheem in the context of believers and He even says very clearly:
وَكَانَ بِالْمُؤْمِنِينَ رَحِيمًا
[...] And ever is He, to the believers, Merciful (Raheem). (33:43)
On that basis, many scholars have concluded that Rahman is expansive in meaning to cover both believers and disbelievers while Raheem is specific to believers. Another way of saying it is that Rahman refers to the mercy in this world which is immense while Raheem is about the consistent mercy for believers in the world and Hereafter.
As for where to find "factual linguistic information," I looked at many tafasir, most of them in Arabic. Perhaps Arabic sources aren't that useful for you but the Tafsir of Ath-Tha'labi for 1:1 and I'rab Al-Quran wa Bayaanoh were useful to me in this case.
For an English source, you can look at the Lane Lexicon. You can find the page on "رحم" here. Although the language is slightly confusing, a lot of what I said in this answer is also present there in the entry for the word Ar-Rahman.
There is also an explanation by Nouman Ali Khan here.