Okay... first minor or major. Minors literally cannot be besieged and cannot be out of supply inside of a city ever period. Majors do care about supply to varying extents depending on difficulty. It's pretty easy to keep units supplied if they are bottled up in a city though as cities can output a lot of food etc. I don't think sieges ever affect trade for anyone (it's a loose siege spread over many kms so some global traders can always slip in and out). Cities can also produce metal, normally by scavenging ruins if they are on ruins though you could luck out and get a metal deposit, and obviously cities invariably contain IP assets to ensure they are defended. What resources would you expect this city to not be able to produce or blockade run? Depends on the habitability of the planet right? Siwas are pretty much impossible to starve to submission. It may be possible on less hospitable planets.
Okay moving on. You do get a concentric attack bonus. It is the first bonus listed on the combat odds screen and it clearly defined in the manual. It scales based on angles of attack to 100% for an all-round attack with mixed units. Units entirely in the same OHQ get a bigger bonus and yes you can have up to 7 units per OHQ so a single OHQ can fully surround with a unit spare. The bonus here is 200%.
Adding more units can have counter-intuitive results both because the game generates odds based a one simulated combat round using all the data available to the player. There are a lot of modified and weighted rolls in combat so combat situations can be highly chaotic (as in chaotic systems though obviously battles are highly chaotic in the colloquial sense too)). Chaotic combat scenarios will have wide results swings from each addition or subtraction because the game simulates a new round each time. Also more is not better. There are penalties for attacking with too many units and some units have big penalties attacking into cities. The game may be accurately reflecting the fact that your attack, overall, is actually less favourable (though not necessarily less likely to win) with additional units.
The answer is artillery, encirclement, human wave attacks, bypass (though this is a capital) or technical development. Keep hitting them turn after turn with cycling units, to ensure readiness and morale recovery, that are in perfect supply and have good casualty replacement. They will crack. No different to, you know, actual urban warfare against a determined opponent with supplies.
Personally I have never had problems, so far, taking cities. Then again, I use a lot of foot infantry who get no additional malus for city attacks (maybe there are no maluses for city attacks and only base terrain is used... can't find it in the manual and I don't have a city I can attack right now) though they are poor offensive troops in general.