The (traded) company may have raised money through stock,
That would be stockholder equity under "issued shares" and "additional paid-in capital"
but maybe it also issued bonds,
That would be under "long-term liabilities", but note that issuing bonds does NOT change stockholders' equity, since liabilities (debt) and assets (cash) are both increased equally.
has profit this year, etc.
That would be in stockholder's equity under "Retained Earnings"
So they are included in the equation, just not under the same terms you're looking for.
Likewise(?), stockholders' equity is used when trying to valuate a company... but I don't see many mentions of bonds, etc.
Suppose a company had no assets other than $1 million in cash. What would the company be worth? Now suppose it issues $1M in bonds, and now has $2M in cash. What is it worth now? The reason the accounting equation holds is because by definition, the equity of the company is what it owns (assets), minus what it owes (liabilities). Everything else is "equity", just like a home with a mortgage.