When you mention it's 7V between gate and source, I guess it's based on 21.4 - 14.5? Can you help me understand the diagnosis that the transistor has blown from this?
You can imagine a FET as very roughly like a variable resistor (between source and drain), controlled by the voltage between the source and gate terminals.
With no voltage, the resistance is near infinite, open circuit. With enough voltage, which depends on the device, the resistance drops to a low value, anything from one or two ohms to a few milliohms, again depending on the device.
The one in your circuit should be down to around 40 milliohms with 7V on the gate, so near a dead shot - and there should be virtually no voltage between source and drain, so the charger positive is in effect being connected directly to the battery, via the two diodes.
It's not a sophisticated charge control circuit, it has no current sensing anywhere, just the FET as an on-off switch to connect or disconnect the charger. It must rely on the charger being incapable of providing enough current to damage anything.
The laptop power unit has no such restriction and could deliver way more current than the transistor could stand when it switched on, so it popped...
If you look at the graph at the bottom left of page 3 in the transistor data sheet, it shows the typical resistance vs gate voltage for that specific device:
I have a couple of work lights that has exactly the same type of failure - they came with chargers that could only give half an amp, but they used USB connections like phones etc. so should have been OK to connect to any normal USB power source.
The designers apparently did not think of that, and did not include any current regulation. The charge circuits in each failed instantly when I used my normal multi output USB power unit, that I use for phones and tablets. The charge switch in the lights was only rated 0.8A, so virtually any recent USB power unit would blow them...