Photosphere is relatively transparent. Is that right? This book, Astronomy in Minutes: 200 Key Concepts Explained in an Instant, by Giles Sparrow, says the photosphere is a visible surface at first, but after that, it says the Sun becomes cool and then transparent, so I am confused.

Our local star is a fiery ball of gas 1.39 million kilometres (863,000 miles) across. Powered by nuclear fusion, it has a three-layered internal structure (see pages 272 and 286). Its visible surface or 'photosphere' marks the zone where the Sun's hot gases grow sparse and cool enough to become transparent, at a temperature of around 5,500°C (9,900°F), but the Sun's sparse atmosphere or corona extends much further outwards.

I think the sentence highlighted in bold (not highlighted in the original) represents the definition of chromosphere... Is that right?
See the other answer by @RobJeffries for a more thorough explanation. Here I just address the the question of how something transparent can also be visible.
Transparent things can still emit bright light. Under some circumstances it can even approximate blackbody radiation. Think about red hot glass, and then imagine it is much bigger and the glass is now gas.

above: from Glowing Glass

above: from Wikipedia