[RPG] Can Storm Sphere’s bonus action be used on the same turn the spell is cast

Controlling a spell is not casting it

On the first turn, you are right, you can cast Spiritual Weapon (as a bonus action) and a Cantrip (as an action) but not any other spell.

On the subsequent turns you can cast any spell as an action and then use your bonus action to control an already existing spell. In fact, you can have both active and control one of them using your bonus action, while the other one is on standby and still cast another spell.

Note, that Bigby's Hand duration is based on Concentration. This means you will not be able to cast any other Concentration spells if you want to keep Bigby's Hand active at the same time. Spiritual Weapon does not suffer from it.

It would appear that Crawford's weighs in on the cantrip rule is only with relation to spells that are cast with the bonus action, this also made it into the Sage Advice Compendium.

Crawford confirms here.

Question: Can I misty step (bonus), fire bolt (action) and fireball (surge) on same turn? Or need action surge also be a cantrip?

Crawford: In that situation, the Action Surge spell would also need to be a cantrip

Crawford: The rule on bonus action spells pertains to your whole turn, not to a particular action (PH, 202).

PHB p202 Under Casting Times and Bonus Action

You can’t cast another spell during the same turn, except for a cantrip with a casting time of 1 action.

Since Action Surge gives you a whole other action and not a another turn you can certainly cast another spell so long as you did not use a Bonus action spell.

The Sage Advice Compendium also provides clarification:

If you cast a spell, such as healing word, with a bonus action, you can cast another spell with your action, but that other spell must be a cantrip. Keep in mind that this particular limit is specific to spells that use a bonus action. For instance, if you cast a second spell using Action Surge, you aren’t limited to casting a cantrip with it.