What you described IS the schema of the database.
Schema doesn't imply rigidness.
A schema can precisely define a wild lack of structure.
The reason it's important to have it is because it keeps you in the control seat.
If I write some code to sum up account balances, it's going to expect a series of account objects, and they need to have some `.balance` field.
And those fields need to be decimals, because addition will choke if they're not.
Your code implicitly defines a schema, and it's utterly rigid because it will crash if the data structure is incorrect.
Or worse.
Imagine if some of the "balances" are actually some irrelevant field that happens to be a number, or some are missing because some of the JSON misspelled the field name and you skipped those records. Now the result you're processing is silently wrong, and who knows how far the corrupt data gets before someone catches it?
All schemas are enforced rigidly because that's how computers work. The difference is whether you want the DBMS to nag you while you're coding, or whether you'd rather be woken in the middle of the night by an angry customer or boss.
So it's irrelevant whether it exists or not because we don't know it.
Say you have a legacy application you want to rewrite.[1]
If the data is stored in an unstructured way, then the schema is in the code base of the legacy application, and will have to be reimplemented in the new application.[2]
However, if the schema is implemented by the database, then the application can be upgraded relatively easily.
[1] Or an example more suited to modern ears, say you just wrote an MVP and want to do a rewrite now that you have 50 customers on it.
[2] Often in a a bug for bug compatible manner.
The data itself is what would be considered unstructured; basically many dozens of different document types. This is why I chose to store it this way. However, in retrospect, it would have been much better for maintenance, performance, quality, and code-size to have created every document type as a separate strongly-typed table.