Thanks for your screenshot.
I may be completely off the mark but it seems in all this discussion, you're apparently overlooking one crucial detail as you're fixating on the "Incoming" numbers.
That detail is the "Local" part of the supply tooltip. It shows the amount of supply that is available locally in the province itself. These supplies don't need to be brought in via land or sea from the capital, they're just "there". Think of them as food, medicine and fuel produced and/or stored in the province. Even if the province is completely cut off from the capital, these local supplies are still available in the province.
Look again at my last example above, there are 3 garrison units sitting in Honolulu. The supply tooltip shows "Local: +5". That means there are 5 supplies available in Honolulu. It also shows the 3 garrison units are consuming 1.30 supplies. Since 1.30 is lower than 5, the units only need to draw supplies locally. No additional supplies need to be brought in via land or sea. Since Hawaii is a set of islands, additional supplies, if needed, would require naval convoys. But as you can see in the screenshot next to the supply tooltip, the supply transfer route tooltip shows there are no supplies being transported, there are no convoys assigned to that route. Again this shows that the local supplies in Honolulu are sufficient for the units present there. Does that make sense?
Now back to your OP example with Chinese units trapped. It follows the same scenario as my Honolulu example. The Chinese units are simply using the local supply available and do not require additional supplies being brought in via land or sea. If you didn't attack them, they could stay trapped in their province forever without suffering lack of supply penalties and without needing any convoys at all.
Consider that the standard Chinese infantry division (6 INF, no support, 12-width) consumes 0.42 supplies.
1. In your OP example, we see "Local: +2" for the Ningbo province. Therefore, up to 2 / 0.42 = 4 Chinese infrantry divisions can be supplied locally.
2. In your last example, we see "Local: +3.45" for what looks like Shandong. Therefore, up to 3.45 / 0.42 = 8 Chinese infantry divisions can be supplied locally.
When via convoys was the only way AI could've received supply with its land route cut off.
Yes, but in the OP case, the AI doesn't necessarily need to receive additional supplies by sea.
Lastly, in all my comments I spoke in terms of province, while supply is actually handled on a "supply area" basis. The distinction between the two is not important IMHO for this discussion.
Sorry for the wall of text.