I would like to understand if the container used to cast Magic Jar should be considered as a magical item and can't be used for other spells/abilities that require a "nonmagical object", such as True Polymorph. I would say no because the Sage Advice Compendium (pp. 17-18) lists some criteria that do not seem to match with this case, but I am not totally sure.
If you used a nonmagical spell component, it remains nonmagical
It should be noted that magic jar does not restrict the spell component to only nonmagical things. You could use a magical item with a gem worth at least 500g and it would qualify, as the spell only lists as its material components:
a gem, crystal, reliquary, or some other ornamental container worth at least 500 gp
Once used, the spell does not turn the item magical. This is because the spell does not say it becomes magical, so if you started with a nonmagical component, it remains nonmagical.
Contrast this with the magic weapon spell, which says:
You touch a nonmagical weapon. Until the spell ends, that weapon becomes a magic weapon with a +1 bonus to attack rolls and damage rolls.
Or, the holy weapon spell:
If the weapon isn’t already a magic weapon, it becomes one for the duration.
If the spell is intended to turn an item magical, it will say so. Magic jar doesn't say so, so it doesn't happen.