Usually, when stock prices are shown, it is clear how recent the displayed prices are. For example, real-time or 15 minutes delayed.
Looking at the stock prices on Kagi, it would be normal for the user to assume the same. The fact that it is from the close of the last business day would be surprising and shocking if they went to another site that listed relatively real-time stock prices.
There is plenty of space if a note like "(xx/xx/xxxx closing price)" was to the right of the price in the size of the price change.