>>1839251RealTimeTrains is your best bet. There's no way that I know of to search 'all routes operated by Class XXX' but, if you look into departures from stations, it'll identify which train is planned to operate that journey.
Random example:
>https://www.realtimetrains.co.uk/service/gb-nr:P99362/2022-08-14/detailed...so I guess if you had a specific train in mind, you could take a look at its Wikipedia entry, find out which operator uses that kind of train, and sort of work backwards from there; 'EMR use 158s on their regional trains, look what stations they serve, departures from their stations today, ah hah' and so on.
