The supply system while a big improvement over the very simplistic practically non-interactive previous system is not perfect. And it's very opaque. It took me a long time to figure it out as a result. The UI for it isn't very good (clear) either (HOI4 issue since 2016). A lot of stuff isn't explained really.
However, even if you run out of supply, the penalties on your Divisions aren't that bad. Nowhere near what they should be realistically imo. You get a moderate debuff at most it seems like. Don't think I've seen it higher than like -35%.
One BIG thing that leads to confusion is that even with a Supply Hub in range and at full Motorization, even with full Infrastructure, even with adequate railway line connection, it can still be possible for your units in the area to not be fully supplied. It's literally impossible to fully supply units sometimes on certain tiles and then game doesn't explain this at all. The only way to get them fully supplied is to use air supply or build more supply hubs. You have to overlap them basically. It's a confusing and weird design but that's how it works.
Ideally and logically you should be able to upgrade the supply hub to a higher level (beyond level 1) and increase the amount of Trucks operating at the supply hub in order to meet your units' supply needs in the area. But for whatever reason the Devs decided not to do that and went with a different design.
Supply also affects naval units somewhat but it's not really explained anywhere in the game as far as I can tell.
Also of note, even though they added a detailed supply system to the game. They still left the old legacy "state/local supply" mechanic in the game. So you often don't even need to build a supply hub or improve infra or anything if you don't have a lot of units in the area. Obviously this doesn't really make sense in a World War 2 game as modern armies can't just live off the land like ancient armies did. It also undermines the entire point of having a supply system, but again for whatever reason the Devs left it in the game. Maybe to help the AI idk.
There are also disruption factors that effect the amount of supply getting to a tile (weather, terrain) and possibly the range? But the game doesn't directly show you this. There's no map mode for it or numbers provided in tooltips or anything for it. That info is hidden for whatever reason. This goes to the opaqueness issue I'm talking about. There really should be separate map modes and tooltips for all this stuff (state supply, hub supply, weather disruption, terrain disruption, combined supply, allied supply, etc)
Also beware, your allies will flood your territory with units and literally just suck up all your supply. Because it seems to simply be shared equally across all friendly units in the area. No priority levels. You can completely turn off allied supply on the hub, but then their units won't have any.