Whatever system you use will boil down to a few basic principles
When delivering a load of cargo going to one place, a single
larger transport vehicle is cheaper and equally fast per unit as
many small transports.
When delivering a load of cargo to many places, many small
transports is both faster and cheaper per unit than 1 large
transport making many sequential stops.
The less you need to pack and unpack between transports, the faster and
cheaper per unit your transport is.
So, the first part of answering your question is figuring out the optimal layout. If your city has a single massive port for ingoing and outgoing logistics managed by a single entity, then you can minimize the overhead of getting supplies in and out of the city to begin with. Instead of each corporation having their own distribution center, in your city you minimize waste on underloaded bulk freight by making them all share. This central hub would basically function like an Amazon warehouse just being a catch-all for all goods and services. From their you do not necessarily want to unpack all of your freight containers yet though. If you have an industrial district in one place, and residential district in another, then you can send individual freight containers closer to their final destination by just loading them right back on smaller subway trains to district hubs. From those hubs, cargo can be further divided up and sent on even smaller subway carts bringing goods directly to people's homes and buisnessess.
Your Regional Subways need to accommodate train car containers from 8x8.5x20 ft to 8x9.5x40 ft to make sure you never need to unpack one to get it to its right district and remain compatible with all international standards of shipping container sizes.
Your District Subways however are not your normal train system. They are more like tracks for self propelled mining carts that range in size from a shoe box for small parcels up to 4x6x12 ft carts designed for construction materials and large furniture. This way, instead of loading up a large truck and carrying your things to a lot of other stops before arriving at your home, you send the right sized vehicle for the job to pickup or deliver goods in just 1 stop.
Then every home or business has a basement that functions their own private receiving station. You get home from work, and your groceries are just sitting down there in a cart waiting for you to unpack it.
Why subway carts?
Pneumatic tubes: They require a seal that causes more friction than wheels and more precise construction to make; so, the cost to make and operate them is more than traditional subways.
Flying Drones: They require less infrastructure, but are much more expensive to operate. Carts passively resist gravity by sitting on the ground, but flying drones need to expend a constant energy just not to fall. They are good for premium expedited shipping of small parcels, but if you are moving around heavy bulk things like furniture, garbage, plywood, etc. then you are wasting a lot of money on them
Conveyor belts They will either need to be way overpowered for most of what they transport or they will need to have complex transmission systems distributed every few feet which will break often due to constant gearing up and down. Either way, they are not as efficient.