What limitations does the trial balance have over the formal financial statements.

Trial and balance is only a worksheet, a statement of ledger that does not guarantee you have no errors. A formal statement should be right to the point and easy to read.

Since statements can be done off an adjusted trial balance, if the trial balance has errors, so will the financial statements. So that reasoning doesn't work.

And financial statements have absolutely no guarantee at all that they don't have any errors. They are only as good as the account balances they came from.

The main difference is that a trial balance is merely listing the balances for each account that you have, in the order of those accounts. But the main separation between balance sheet and income statement isn't there. And sub-categories aren't there. (e.g. current assets vs plant assets) Sub-totals and other calculations of different types of things are not there. Like total operating expenses, or gross profit, or the book value of a plant asset, etc.

While the accounts on a statement are listed in the same basic order as on the trial balance, the statements are organized into sections and have certain calculations and sub-totals on them. A trial balance does not. Which is the main difference.