I’m no historian, but I am a geneticist with a history undergrad and figured I might as well try to chime in. Mods, please forgive my very un-historian-like inline citations.

Yes, Y. Pestis is firmly accepted as the cause of the Black Death. Analysis of ancient remains from plague graveyards confirmed this beyond reasonable doubt a few years back - researchers essentially ground up ancient tooth pulp and sequenced the DNA they found therein, which was mostly human DNA of course but also included DNA from y. Pestis, confirming the presence of the bacteria at the time of death. Consistent presence of Y. pestis in plague victims leads us to a broad consensus that it was the causative agent in the Black Death (and subsequent pandemics that continued to pop up in Europe).

Here’s a general review of the topic:

https://www.journalofinfection.com/article/S0163-4453(12)00277-0/fulltext

It’s worth noting that Y. pestis has also been confirmed by similar methods as the causative agent in at least two additional major pandemics: the plague of Justinian that ravaged the near east starting around 540 (see e.g. https://www.ncbi.nlm.nih.gov/m/pubmed/24480148/?i=4&from=yersinia%20pestis%20justinian), and the ‘third pandemic’ in China in the 19th century that finally allowed scientists to isolate and describe the bacterium (including Alexandre Yersin, hence the name).

Current research focuses on finding other instances of Y. pestis in archaeological sites (see https://www.ncbi.nlm.nih.gov/m/pubmed/30528431/?i=1&from=yersinia%20pestis%20neolithic for a cool paper on Y. pestis in Neolithic remains), tracking current outbreaks (https://www.ncbi.nlm.nih.gov/m/pubmed/29897940/?i=5&from=yersinia%20pestis%2019tu%20century), or figuring out the exact relationship between outbreaks - which were direct transmissions from other plagues, which represented new emergences of the disease into humans, and the relationship between different strains of the disease throughout history (see some excellent old-school academic chair throwing at https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(14)70878-3/fulltext)

I suppose so, and I posted very brief bibliographical notes on the similar question thread, what authoritative and up to date papers can I read about the cause(s) of the Black Death?

Still very hotly debated, 2010/11 can be regarded as a kind of watershed for this debate in favor of Y. pestis hypothesis, with help of DNA studies. Since then: '......I have counted at least 24 separate studies - representing 32 grave sites in five European countries - that independently confirmed through paleomicrobiology that Black Death was indeed plague'. (Aberth 2018: 246).

I suppose it would be almost impossible to confute these samples, and even the most rigorous anti Y. pestis specialist, Samuel Cohn, seems now to reserve himself to argue against the rat-flea thesis, not the DNA identification of Y. pestis itself (Link to his comment in tertiary article of National Geographics in 2018).

Notes also that most of anti Y. pestis historiographical counter-arguments, conveniently summarized in [Pobst 2013] (AFAIK hers is the latest historiographical academic article concerning the Black Death by any anti Y. pestis specialist), had already throughly been refuted by the historiographical surveys of pro Y. pestis specialists like [Benedictow 2011], and its latest lite version, [Aberth 2018].

References:

• Aberth, John. Plagues in World History. Lanham: Rowman & Littlefield, 2011.
• ________. ‘Ashes to Ashes, we all fall down: The Black Death’. In: Id., Contesting the Middle Ages: Debates that are Changing our Narrative of Medieval History, pp. 243-315. London: Routledge, 2018.
• Benedictow, Ole J. What Disease was Plague? On the Controversy over the Microbiological Identity of Plague Epidemics of the Past. Leiden: Brill, 2011.
• ________. 'Yersinia pestis, the Bacterium of Plague, Arose in East Asia. Did it Spread Westwards via the Silk Roads, the Chinese Maritime Expeditions of Zheng He or over the Vast Eurasian Populations of Sylvatic (Wild) Rodents?' Journal of Asian History 47-1 (2013): 1-31.
• Pobst, Phyllis. 'Should We Teach That the Cause of the Black Death Was Bubonic Plague?' History Compass 11-10 (2013): 808-20.

[Edited]: fixes typo, and makes all Y. pestis italic.