Server app, syncing websites, two way data exchange

I am planning a prototype for an installation that involves at least two computers using web speech API synthesis/recognition alternatively, to listen and repeat each others words.

1 - Pc1 emits text to speech with content "x" while Pc2 attempts to speech recognize the content 2 - the other way around 3 - etc...

This pingpong game of speech between the computers should be semi-controlled.

For example, the game could be arbitrarily stopped in order to feed fixed sentences into one of the computers at certain moments, and some behaviours should be programmed in particular case scenarios such as one of the computers failing to speech-recognize.

JS is what I can handle, and as this should happen in sync, I assume each computer would connect through a web app to a common local server that would be reading and sending data from/to those web apps.

I imagine this type of scheme may be common and would like to ask here for any advice on where to look in order to learn how to plan it, and what JS related technologies available can do that.

I acknowledge this is a very open question to the extent that may not be accepted, but after researching on the syncing subject, I did not achieve much, so I thought posting to SO may help.

Please let me know how to improve the question.

Thank you very much for any help.