The two fast Brighton Services from Victoria are operated by (the) Gatwick Express (brand).
All trains branded Gatwick Express, Thameslink or Southern are operated by GTR; GTR is the train operator and the other names are merely brand names.
Likewise as an ordinary passenger how would I find out which Thameslink trains have counted place reservations? That is work through again all of the points in the preceding paragraph
You are overthinking this; most people book the itinerary they want, and then go with it.
If you are not offered the desired itinerary automatically, there is the opton to specify additional via points and/or avoid points and/or additional interchange time.
And as a supplementary, the train in question was cancelled! What are my options? Find another Thameslink train that does not have counted place reservations? That is work through once more all of the points in the preceding paragraphs
If the train is cancelled you may take the next appropriate service; this has nothing to do with whether or not trains are reserveable. If you are ever in doubt what your options are, please create a new thread and state the ticket(s) held, the original planned itinerary along with any other relevant information (e.g. can you depart earlier, if you've not yet set off).
The forum's rail ticket site did alert me by email re the cancellation. And helpfully told me to take the next service matching your ticket route and operator restrictions. Although I had not grasped that the restrictions meant that I had to find the next Thameslink train that did not have counted place reservations?
That's not the case.
The forum's rail site did flag up that I might not make the connection into my booked GWR service from Paddington to Carmarthen. GWR only serve Carmarthen every two hours, and it was a GWR Advance, so probably not valid on Transport for Wales Trains
If the delay to your journey by awaiting the next GWR service would be over an hour and this could be minimised by taking TfW, then your ticket should be accepted; I would ask GWR/TfW this, and if they refuse, you can either accept the delay and a huge Delay Repay payout, or alternatively you can buy a new ticket on TfW if they won't accept the original, and you can bill this to GWR.
Actually the forum's rail ticket site did not grasp that I had deliberately specified extended connection times when I made by booking, to include 30 minutes or more "performance and pathing allowances" in my own journey. So loads of spare time. And indeed these allowances were set so I could stock up in Marks and Sparks at Paddington station with enough to sustain me to Carmarthen. However I did not set up my "performance and pathing allowances" to allow for me finding another Thameslink train that did not have counted place reservations
If you think the forum's site hasn't acted correctly, please provide all the relevant details incuding the search parameters, and let us know what itinerary you were offered and how you felt this was deficient. It would be best if this was done in a separate thread.