Pr.677 was conceived and defined in Soviet times, so the post-collapse Russian budget had little to do with its size (just with the delays...). If overall capability is similar to a Kilo at 70% of a Kilo's displacement and recurring cost that's a success, and it could be even better if the planned fuel cell AIP plant was funded and implemented. Which is what the "new" SSK project is likely to be all about - I suspect they aren't going to re-invent the wheel (maybe plus an x-stern - in any case, don't expect size to increase, if at all, beyond the requirements for adding the AIP system!).
FWIW, Polish experience found the Kilo far too bulky to manoeuvre properly in the shallow, confined waters of the Baltic (which is a close match for the Yellow Sea in several respects). It's no accident either that modern Swedish and German SSKs designed for this environment are all about the same size as Pr.677. The entire East and South China Seas are each smaller and on average shallower than the Black Sea, and it's not entirely due to politics that you don't ever see Russian SSNs deployed in the latter...
Yellow Sea might be shallow but East and South China Seas are deeper than the Black Sea at their maximums.
Maximum Depth:
Baltic Sea - 1506 m
Black Sea - 7365 m
Yellow Sea - 499 m
East China Sea - 8858 m
South China Sea - 18,238 m.
The Black Sea is not even close to the South China Seas. In fact, the South China Sea is deeper than the Mediterranean (17,280 meters).
But of course, this is maximum depth, a big portion of the seas are going to be much shallower.
The modern Kilos are thrown into the Black Sea, and operate in the Med, I see likewise for the Kilos and the Yuans in the East and South China Seas. Vietnam already operates Kilos in the South China Seas, and appear content with it.
Modern attack submarines might have a test depth of around 400 m to 500 m, with a crush depth of around 700 m. So even the deeper parts of the Yellow Sea may already be enough for nuclear submarines. Given that submarines the size of the Kilo and the Yuan can operate fully in the East and South China Seas, I don't think its economical to develop a submarine just to operate in the shallower areas of the Yellow Sea and near the Chinese coasts.
To give some more context.
Submerged Displacement (off from Wiki)
Type 212 - 1800 tons
Gotland class - 1600 tons
Song class - 2250 tons
PR 677 Lada class - 2700 tons
Type 214 class - 1800 tons <--- This one is being built by South Korea, which is expected to operate in the same East China and Yellow Sea waters.
S20 (export Yuan) - 2300 tons. <--- sold to Thailand and expected to operate in the South China Seas.
The 212, 214 and Gotland class are even smaller the PR. 677, which itself displaces more than the Song and the export S20. To create a new small SSK, would be like recreating a Song with AIP, which only leads to a scaled down Yuan, which is therefore like an S20. I don't see the benefit of doing this just for the Yellow Sea, when you still have Songs, and antisubmarine assets like Type 056A to patrol these areas.