PHB describes the downsides of wearing an armor you are not proficient with:
Armor Proficiency.
Your class gives you proficiency with certain types of armor. If you wear armor that you lack proficiency with, you have disadvantage on any ability check, saving throw, or attack roll that involves Strength or Dexterity, and you can’t cast spells.
However, a shield is not armor.
The Spellcasting chapter says about armor explicitly, and not shields:
Casting in Armor
Because of the mental focus and precise gestures required for spellcasting, you must be proficient with the armor you are wearing to cast a spell. You are otherwise too distracted and physically hampered by your armor for spellcasting.
The disadvantages are the same as wearing regular armor you lack proficiency with
(Note, I used the basic rules pg.44 as a reference, but the information should be the same as in the PHB, pg. 144)
You claim that shields are not armor. I challenge this assertion. Shields are not body armor (as noted in this answer on the first linked question). The answer on the first linked question is pointing out that all body armor changes how AC is calculated, while shields give a flat +2 AC.
However, shields are still listed in the armor table along with all light, medium, and heavy armor. The section title that you quote is “Armor and Shields” and the section begins:
Anyone can put on a suit of armor or strap a shield to an arm. Only those proficient in the armor’s use know how to wear it effectively, however.
Additionally, shield proficiency is noted in the “armor proficiences” section of the class description.
Based on the fact that shields are lumped together when talking about armor in the armor table itself, in the beginning of the preceding section, as well as in the armor proficiencies of the class description, shields are meant to be considered armor. Thus, whatever disadvantages come from using armor that you are not proficient with also apply to using shields if you lack proficiency.
As an aside and a note on your second linked question, just because a shield does not interfere with the Draconic Resilience of the sorcerer, doesn’t mean that the sorcerer doesn’t need to get a shield proficiency from somewhere else, like multiclassing, to use it effectively.