Nothing weird in your situation, the supply in Nice just sucks, it's got terrible infrastructure.
So how to read the supply numbers from the Screenshot:
Starting with Milan:
84/134 - easiest to understand, total supply vs available supply
160 & 27/24 - the top number is the maximum incoming overland supply, the bottom are "maximum infrastructure (includes those being built"/"current infrastructure" - these are used to determine incoming/outgoing supply however you also need to know how many states are in the supply zone. Milan supply zone has 2 states in the base game but it looks like Kaiserreich expands it to 3, so average current infrastructure is 8 in the supply area. This means for incoming calculations it can receive 8 * 8 * 2 = 128 supplies, and it will give 8 * 8 / 2 = 32 supply to outgoing areas. Since you control 28.5% of the border between Nice and Milan you are only receiving 28.5% of this amount: 32 x 28.5% = 9.12 supply.
24 & 8 - the top number is the maximum incoming overseas supply, the bottom is the largest naval base. To figure supply you will also need to know the 2nd & 3rd largest naval bases, however in this case it looks like the supply area has only one base. The amount incoming and outgoing is 3 times the total size of the 3 largest bases or ( 8 + 0 + 0 ) = 8 x 3 = 24 supply. This isn't used as overland is better.
Now with Nice:
35/29 - total vs available
71 & 17/14 - the supply area of Nice is 3 states, so the 14 total infrastructure divided by 3 states gives 4.66 average infrastructure. This gives incoming supply a limit of 43, combined with Milans 32 to get 71 (I know, the math is off somewhere). This is your problem, Nice has absolutely terrible infrastructure, particularly in Europe.
6 & 2 - the naval base in Nice is size 2 so you get 6 supply overseas. This isn't used as overland is better.
Now the one thing that the game wont tell you is that each supply area has a base supply that is used to calculate local supply. Nice is 9 (with 6 more from victory points) and Milan is 15 (with 5 more from victory points).
So your supported number is:
9 base x 28.5% control = 2.56 + 2 from Nice victory points = 4.56 local supply
4.66 average infrastructure x 4.66 x 2 x 28.5% control = 16.25 incoming supply (hard to say how this is calculated without knowing exact infrastructure numbers, it seems that the average is actually 5.34 for the calculation)
9.12 incoming from Milan based on the Milan infrastructure
The thing though is you have troops stationed in every single tile of Nice, while you only have something like half to a third in Milan, so of course you are going to be using a much larger share of supply compared to Milan. That being said, if Nice had the same infrastructure as Milan you would have about 50 supply, as incoming supply would increase to about 36 plus the 9 from Milan.
You tell me

My thread from 2017
Lol, now that's an actual wonky situation. You went from getting the full local supply because you had a separate supply zone to part cause of the border situation. You're actually getting more from the incoming province but less from the local province.
The solution would really be to grant local supply based on how much % of the state you actually control vs full or border based as it is currently. It would have dropped the amount in your initial situation but would make more sense than receiving 100% of the supply areas supply. Not sure if it would help the after situation either as the top area with 5/15 is part of the same supply zone so you would be hitting max if it was all treated the same and it's receiving the full 9 from the local supply. In both cases your probably getting more supply than you should have if it made sense...
It wouldn't help the Nice situation as his # would actually drop based on % state ownership as well and the local amount is minuscule compared to the incoming.