The equity is merely an estimate; it’s no longer a traded company so a public valuation is not applicable.

Even for private companies, though, the valuation matters for all sorts of events that might happen in the meantime: employees with equity still might be forced to sell if they quit their job, so that value ends up actually supporting real transactions trading equity for cash, income tax will look to the fair value at the time of vesting (or grant, in some cases).

And the debt is secured by the $19B valuation, so it’s not in addition to the equity; the company is “worth” $19B but caries a debt burden of $13B making it’s liquidation value $6B

I don't think this is right. In a typical leveraged buyout, the debt is secured by the assets of the company itself, not by the equity in the company. In other words, the money is owed by Twitter Inc. (and secured by what Twitter owns), not by Twitter's shareholders (and not secured by the shares themselves).

The old owners got $44 billion. $13 billion came from lenders, not new shareholders. New shareholders agreed to the deal because it allowed them to pony up less money for 100% ownership of the corporation, but the corporation itself is now more burdened with debt. The enterprise value, however, is shareholder equity plus debt, so the enterprise value itself doesn't change with the debt. That's why I added the total debt to the total valuation of the equity.