... Is there a computer or other platform application that will allow the recording of multiple passenger station train announcements and has a selector for playing the appropriate announcement at the appropriate station through a speaker in that station?
...
Appears you envision this as a "centralized" system with a single computer (tablet/laptop/whatever) and multiple speaker cables going to individual stations. I'm not sure such exists for the application at hand.
As others have suggested there are many products that are individual sound modules that record a sound and then play it back when triggered by a push-button switch. Prices are all over the map based on features. Think of those audio greeting cards where you can record a 10-second (or whatever) custom message, "Happy Birthday Grandma, we love you!". The speaker is tiny, the volume is tiny, the battery is tiny, the audio quality is so-so, the length of time is short, etc. But it fits in a greeting card! This would be "free" if you re-cycle one, or they can be purchased for a few dollars.
I'd say the "sweet spot" in these recordable sound modules is in the $30 range with a larger speaker, longer sound recording time, and so on. But this would be one module per station. There have been many OGR threads on these modules. If this configuration works for you we can identify specific examples if you share a bit more about the requirements... how many stations? how long are the announcements? do you already have the sounds and in what form (MP3 file, on a cassette tape, on a vintage Noma talking-station record, etc.)? do you need to adjust the volume?
Note that the Universal Sound Module described in an above post can be triggered wirelessly! It's a bit more expensive and you'd still need 1 module per station which can add up the $ if you have a gaggle of stations.
And there are variants in-between...especially if you're willing to do DIY wiring and such.