Guess what this song is! :)
जन गण मन अधिनायक जय हे भारत भाग्यविधाता पंजाब सिन्धु गुजरात मराठा द्राविड़ उत्कल बंगा विन्ध्य हिमाचल यमुना गंगा उच्छल जलधि तरंगा तव शुभ नामे जागे तव शुभ आशीष मागे गाहे तव जयगाथा
जन गण मंगलदायक जय हे भारत भाग्यविधाता जय हे, जय हे, जय हे जय जय जय जय हे!
Bonus points for saying who wrote it!
The first 3 words give it away. The Indian national anthem written by that guy whose name starts with Ta-something. I won't cheat and look it up, but I can give you an interesting fact that you may already know: He also wrote Bangladesh's anthem, and had some sort of contribution to Sri Lanka's anthem as well (if I'm not mistaken), making him the only person attributed to three national anthems.
Why "of course"? Can you understand it as Hindi? Why is it that Hindi speakers need to ask for the meaning? i.e. https://www.quora.com/What-is-the-meaning-of-Indian-national-anthem-in-Hindi
Tagore was writing in an artificial form of Bengali that was SO Sanskritized -- we could also say "sanitized" because he seems to have purged the language of the Persian vocabulary that makes it what it is -- that what we're left with is a sequence of Sanskrit sounding phrases. People educated in Sanskrit roots and such, no matter if their speaking language is Gujarati , Hindi, Nepali, Punjabi, Bangla, whatever, can get something out of the song because they recognize those Sanskritic forms from their education. But it doesn't flow together as Hindi as far as I'm concerned.
That is true, but it would be largely unchanged in any North Indian language anyway, simply because as you said, they share many of the same Sanskritic forms of words. However, this translation is still in Old(or Sanskritic)Hindi, because the Bengali form is slightly different.
What is "Old Hindi"? What exactly makes this the "Hindi" form versus the "Bengali" one?
There is no grammar here. No sentences. It is all just nouns and adjectives that have a Sanskrit root. Hindi and Bengali both have Sanskritic roots, but both languages, as commonly understood, use many more Persian words in normal use, and the words that are of Sanskrit origin are evolved to different forms than what we see here.
It's like composing something in Latin. Spanish and Italian speakers will recognize a lot of the Latin words if they are educated in such things, but it will be neither Spanish nor Italian. "Quid pro quo e pluribus unum Catalan Sicilia Italia Galicia Christo redemptor Amen Amen per capita largo annum, lol."
Ask a Hindi speaker if they understand this. I doubt they will unless they have been educated specifically. See my link above, where Hindi speakers are asking for a translation because they don't know what the heck the song means!
It works as an anthem precisely because it is not any one language, but just words that are equally comprehensible (or not comprehensible) to speakers of all the North Indian languages.
Not to take anything away from Tagore in general, but he has done no favor for the Bengali or Hindi languages by making up this artificial language for this.