None, in my opinion. PLA is nowadays a much more professional force. Considering Taiwan is unlikely to hold out for long, it is questionable it would ever need to conduct a large scale draft like Russia did in Summer 2022. Taiwan's strike assets are too small to cause any damage to morale (let alone much physical damage) by hitting civilian targets on the mainland.
If there was to be any unrest due to the war, it might be because of economic damage caused indirectly by the war (*hypothetical* example: severe decline in trade with US). However, it should be noted that Russia, which was fairly interconnected with the West prior to February 2022, took such damage and is more or less fine despite having taken little to no measures to alleviate this danger previously.
In contrast, China is actively trying to eliminate foreign dependence in every sector of the economy. Not only would economic damage be *relatively* limited, but any unrest would probably be sporadic. Although the PSP, MSS, PAP would need to have higher vigilance, they probably would not need to do anything they aren't already doing right now.
Looking at it from another perspective, the anti-war movement in the supposedly free world, especially the United States, comprised a tiny portion of the populations of each country involved in that invasion. If that is what happens in the US when it invades a sovereign nation, resistance to war in China when it is seizing an island whose formal name is literally (Republic of) China is unlikely to bring about any moral qualms in mainland citizens, at least not any to the extent that huge numbers of people would actually go out and protest the conflict.
If by "internally [in China]" you mean in Taiwan after it is a practical part of China again, that's another question but it might be outside the scope of the thread.
