If there are no advantages to making it smaller, why was it made smaller?
677 is not that much smaller.
The 677 is already 67-72 meters in length, the Kilo is around 70 to 73m, and the Yuan is around 77 meters. The difference is that 677 has a smaller beam, 7.1m, with a 6.5m draft. Kilo has a 9.9m beam with a 6.2m draft, while Yuan is 8.4m beam and 6.7 m draft.
In what way does the 677 Lada gives it a tactical or operating advantage over the Kilo and the Yuan in any of the bordering seas to China? Is there anything in particular about its design and size that makes it better to operate in shallower seas?
677 is certainly not in the Type 212 class of size, which is 56 meters, or the Gotland class, which is 60 meters. Both Gotland and the 212 have these X shaped fins to let them operate in very shallow waters that can be useful for dropping special forces. The 677 doesn't have this, assuming there is actually some benefit in using X-shaped fins.
677 is "smaller" in the sense that its crew size of 35 is smaller, with the Kilo at 52. The Yuan though, is only at 38, and given its size, and that's going to be generous and more comfortable for the crew than either the Kilo or 677. Crews on the Gotland and the 212 is probably around 22 to 27 if I remember correctly.