The IN chose technology over saving time. So the Nerpa is done, it will be pushed into service in the Russian navy after a refit. Otoh, we are very likely looking at leasing the unfinished Irbis, which came after Nerpa. So it's practically a new hull too. Plus a lot of the new submarine's internals will be Indian systems, stuff that's meant to go into the Indian SSN program.
So both the Kilo class upgrades and the leased SSN will have a lot of Indian tech.
Okay so I am not claiming to be 100% right but this is what I found
Amur shipyard.
1. K-284 Akula (1984) ; scrapped in the period between 2004 and 2008 at Zvezda...
2. K-263 Barnaul (1987); scrapped in floating dock PD-14 in the period 2018/19
3. K-322 Kashalot (1988); in the process of scrapping at Amur shipyard(was first thought to be the submarine getting ready for us)
4. K-391 Bratsk (1989); from 26.09.2014 in Zvezdochka repair plant, inactive. Planned to be modernized to 971M project. But upon inspection it was found that the submarine is in very bad condition and not fit for renovation. (This was the 2nd hull after K322 inspected by India)
5. K-331 (1990) ; name REMOVED because one submarine of the project 636.3 has took the name "Magadan", or B-602 Magadan on 01.11.2019. K-331 is in overhaull and this submarine will become the submarine of the project 971U according to russian MOD and it was said that the overhaul will be completed in 2022. But since the name has been removed , I think that this one might be getting ready for India. But if it's this one, then it's supposed to go into trials by 2022 end. But one problem I think is that when it started its modernisation, it was for Russian Navy. So if it's for Indian Navy, then the refit might extend beyond 2022.
6. K-419 Kuzbas (1992) ; Modernized and returned to service in march 2016. Project 971U.
7. K-295 Samara (1995); from 26.09.2014 in Zvezdochka repair plant, inactive. According to russian MOD the deadline for the return of this submarine to service has not been determined because the complete old equipment has been removed from the submarine, while the scope of modernization work is significantly higher than planned. This submarine will become the 971M project after modernization is finished.
8. K-152 Nerpa (2009); inactive, in august 2021 it was delivered from Indian navy crew to the crew of the russian submarine K-419. It will probably be handed over to RN, but who knows when.
SEVMASH ;
1. K-480 Bars (1988); scrapped by 2010
2. K-317 Pantera (1990); probably in service
3. K-461 Volk (1991); inactive, from 2018 in Zvezdochka and it is planned to be upgraded to the 971M standard, just like the K-328 Leopard. It is planned to be handed over to the Russian Navy in 2023. Project 971M.
4. K-328 Leopard (1992); taken out from the slipyard in Zvezdochka on 26.12.2020 and the submarine is scheduled to be returned to service in 2022. Project 971M.
5. K-154 Tigr (1993); from 2019 in Nerpa repair plant and overhaul will be completed by 2022. This would not happen almost certainly because submarine has not yet been launched and this submarine will not be modernized to 971M standard.
6. K-157 Vepr (1995); returned to service in 2020 after repair, active. This is not a submarine of the 971M project.
7. K-337 Gepard (2001); active, project 971U.
And finally the incomplete hull of Irbis. No activity on that.