The SWR» description on Journey Check said "due to an operational incident". The GWR▸ version said "due to a broken down train".
I suppose a car that has run out of petrol could be described as broken down. There are various flavours of broken down of course.
If you look (or looked at the time) at the various online sources of information on yesterday's goings-on, you could get quite confused. SWR and National Rail referred to it as "an operational incident" - I can see that might mean "this is embarrassing, we'd rather not go into details". GWR JourneyCheck, however, said it was a broken down train; well it wasn't one of theirs, was it?
RTT» (or rather its sources) can't cope with trains going in reverse, and struggles when several are so late it's hard to know which train is which; that much is well known. Also, the reason given that we see is only shown for cancellations, not delays, and is only an initial entered code which may be altered later in the more detailed version used internally. But even so, those codes were unconvincing.
The train that was singing "Oh! Mr signaller, what shall we do? I want to go to Bracknell and you've sent me on towards Sandhurst" was 2C46, shown as cancelled from Wokingham "due to an issue with the train crew (TG)". That's the usual code for no driver being available, though arguably it's not the right one (TA and TI overlap with it). There was also a round trip cancelled with this code not long before; that presumably was a staff shortage. The later SWR trains that were turned at Ascot show as cancelled between Ascot and Reading due to the train operator's request (TB).
However, TG also covers driver errors of several kinds. As we saw the last time a train took a wrong turn, the driver is responsible for detecting (from signals) mis-routing and is expected to take action to prevent or mitigate it as soon as possible. At Wokingham, assuming the points were not moved after the train passed the signal (not possible, I hope), the feather lights are there to be seen by the driver before starting (as in bobm's picture). So there will be an internal "TG" incident, but there should be another one coded "OC", signaller error.
GWR trains continued to run, with interruptions, but only towards Reading, and only as many as had got out past Wokingham in time. Those unable to depart Reading were not defined as cancelled and given a reason until the end of the incident (which is normal). When they were, they showed up as OC, though there are also some shown as TG (of course that could be due to GWR's own staff shortages).
Incidentally, the fact that there is still a mechanical signalbox by the station means the driver and signaller could be in direct communication at all times, simply by leaning out of their windows and rasing their voices a bit. So if they had any differences to settle, that could be done directly one-to-one, and if it came to "I'll see you outside" that wasn't far either (albeit against the rules).