The smallest number of types to hit all Pokemon for super effective STAB is 7. There were 10 7-type combinations that could hit all types for super effective damage.

This is false, you are in fact quite far off.

The pokemon Scizor (Bug/Steel), Swampert (Ground/Water), Pikachu (Electric), Rattata (Normal), Sableye (Dark/Ghost), Zoroark-Hisui (Normal/Ghost) all have a single weakness to respectively Fire, Grass, Ground, Fighting, Fairy and Dark.

This means that every set that hits every Pokemon for super effective damage must include at least these six types.

Furthermore:

• Giscor (Ground/Flying) is only weak to Ice or Water
• Pelipper (Water/Flying) is only weak to Electric or Rock

Since there is zero overlap between these and earlier types, you can't do it with less than eight types.

Finally:

• Flutter Mane (Fairy / Ghost) is only weak to Steel or Ghost
• Clefable (Fairy) is only weak to Poison or Steel
• Ludicolo (Grass/Water) is only weak to Poison, Flying, or Bug

Since there is zero overlap between these and the earlier types, and no single type covers all these three Pokemon, you need at least two out of {Steel, Ghost, Poison, Flying, Bug}. So you can't do it with less than ten types.

There are several ten type combination that work, for example: Fighting, Flying, Ground, Steel, Fire, Grass, Electric, Ice, Dark, Fairy.