The Ahom language was lost as a spoken language, but remains in the manuscripts kept in the homes of people who are descended from the priestly class. The Ahom script lacks any tone marks (the same sitaution with the still-living Phake script of the same area), and there are a number of issues with writing "mistakes", but which are generally recoverable thanks to terms being related across Southwestern Tai languages. But also there are things like vowel length, vowel quality, and similar things which are not clear from the script. This is also the case with Phake, for what it's worth, but with a couple thousand speakers actively using Phake, it's not such a problem. It does mean, however, that the Ahom language, if revived, would not be an accurate revival in the sense of actually recovering exactly what it would have sounded like prior to going extinct. Still, there are many efforts by community members, as well as a number of scholars working on the language. I am one of those scholars, albeit in a supporting role.

The culture is also not well preserved. People with traditionally Ahom surnames tend to be Hindu, speak Assamese, and while Ahom still remains as an ethnic identity, with groups such as the (ATASU)[https://en.wikipedia.org/wiki/All_Tai_Ahom_Students_Union]. I personally know a few Ahom people who attend events put on by other Tai groups in the Northeast in order to learn more about the practices, for things such as weddings. But many of the Ahom people I otherwise know do not have anything distinctly Ahom about their cultural practices.

So in the very short version, identity? Yes. Still very much a thing. Culture? Not notably distinct from Assamese culture. The Northeast has been a largely shifting culture for the past centuries, with the Ahom control, Bodo/Garo control, and more recently Indo-Aryan and British control over the area. This has resulted in a lot of cultural transmission and ethno-linguistic contact effects.

Wikipedia is actually a pretty good place for an overview of the history of Ahom control. But much like the Manchu's of the Qing Dynasty in China, upon the fall of their control, their culture was largely absorbed into the (in this case new) majority. As mentioned, linguistic and cultural revival efforts are underway. But in many cases these involve either adopting Thai practices (which is often ill advised but it is what it is) or trying to recover things from the manuscripts, which many people can not read. It will be a long process, but it's under way all the same.

Here is some of the work that has been done and continues: https://eap.bl.uk/project/EAP373