It's not Hindi at all. It's Bengali. Those languages are as different as Spanish and Italian. They don't even look the same, because they use very distinct, albeit related, scripts.
Bengali, which along with Assamese uses the Bengali script (duh), looks like this:
প্রত্যহ প্রভাতকালে ভক্ত এ কুকুর
স্তব্ধ হয়ে বসে থাকে আসনের কাছে
যতক্ষণে সঙ্গ তার না করি স্বীকার
করস্পর্শ দিয়ে ।
Hindi on the other hand uses the Devanagari (aka Nagari) script, as do Marathi, Nepali, Sanskrit, and some flavors of Konkani. Devanagari looks like this:
प्रत्यह प्रभातकाले भक्त ए कुकुर
स्तब्ध हये बसे थाके आसनेर काछे
यतक्षणे सञ्ग तार ना करि स्वीकार
करस्पर्श दिये ।
The Bengali lines are the first four lines of Tagore's poem, of course. The Devanagari lines are simply a letter-for-letter transliteration of the Bengali. The Bengali and Devanagari scripts are pretty much exactly equivalent; each letter in the one has a counterpart in the other, so transliterating between the two is a cinch.
Note that this is a transliteration, not a translation. The lines would not be meaningful in any of the languages that use the Devanagari script. Some of the words would be, either because of the Sanskrit-derived vocabulary common to many Indic languages (e.g., ভক্ত / भक्त / bhakta, which means a devotee) or by happenstance (e.g., তার / तार / taar, which means "his" in Bengali but also means "metal string" or "wire" in pretty much any Indic language; a Hindi speaker looking at the above transliteration would misrecognize तार as "wire").
In iTrans, the lines would be rendered as follows:
pratyaha prabhaatkaale bhakta e kukur
stabdha haye vase thane aasaner kaachhe
yatakShaNe sa~nga taar naa kari sviikaar
A literal translation would be:
Every dawn this devoted dog
silently stays seated by [my] seat
for as long as I don't accept his company
by patting him.
The poem was published in Tagore's 1941 Bengali collection আরোগ্য (आरोग्य / aarogya, meaning Convalescence). Tagore wrote original works in both Bengali and English. He also wrote a cycle of 22 poems, ভানুসিংহ ঠাকুরের পদাবলী / bhaanusi~Nh Thakurer padaavalii, in a pastiche of Brajabuli, imitating the Vaishava Padavali tradition that flourished in the 15th through the 17th C. He frequently translated his own Bengali poems, stories, etc. into English as well. He did not, however, write in Hindi. Many of his works have been translated into Hindi by other hands, but cursory Googling didn't turn up a Hindi translation of this poem.
I don't know why Translated Labs and AllPoetry think this is Hindi. Or at least I do: because ethnocentrism. But that's an explanation, not an excuse. Considering that Hindi and Bengali are each spoken by literally hundreds of millions of people, and are both among the top ten languages spoken worldwide, it's a pretty shocking mistake. The world is simply jam-packed with speakers of those languages, and those websites can't find a single speaker of either to verify which one this is?
It's mind-boggling that the web should be propagating such an indefensible error, and it's good to be able to clear it up. Thanks for this question and asking me to answer it.
Obligatory disclaimer: My Bengali is dreadful, and the translation of the four lines given above probably has deathless howlers in it, so it's strictly AYOR and corrections are welcomed.
Tangentially relevant funny story: my late husband had quite the gift for languages. He began learning Hindi in his forties. He had just mastered the Devanagari script when he and I went to watch Satyajit Ray's মহানগর (Mahanagar, The Big City), at an arthouse cinema. The titles came on and I noticed he was peering at the screen with an increasingly puzzled expression. I leaned over and whispered "It's Bengali." A look of relief came over his face as he remembered that Bengali uses a completely different script from Hindi.