Can it be said "transistor open/closed" and what does it mean?
The contacts in a switch or relay have a mechanical gap between them. The terms 'open' and 'closed' were adopted into general use a long time ago to mean 'contacts apart' and 'contacts together' respectively.
The terms 'open' and 'closed' have not been adopted for transistors, which happen to have no such mechanical gap. Nor were they used for valves, which have a gap between electrodes but is not a moving part in their operation. Transistors and non-diode valves are amplifying devices. Using them as a switch is using a subset of their full gain range (fully 'on' or fully 'off'). So the idea of an 'open' or 'closed' transistor isn't as descriptive or associated with what you see as with electrical contacts on a switch or relay.
There are mountains of examples in the English language of words that are only used with specific nouns or verbs. This case is far from alone.