It is interesting how the phrase's meaning has transformed. Nowadays people generally use it to add emphasis such that the previous statement is an absolute truth with no valid argument to the contrary.

end of statement. nothing more to be said. no exceptions or reasonable argument to the contrary.

Yep, it's a bit of verbal color to add emphasis to a statement. Much like declaring things that are actually quite ordinary and did not fill you with awe but are otherwise positive as "awesome."

In this context, I took "full stop" to mean "end of discussion." As if to dismiss all dissenting opinions and stifle further discussion.

As for the telegraph use, I'm aware of that. I have a background in amateur radio and in college a crusty old engineer taught me morse code to communicate over the maintenance department's secret building-to-building campus telegraph network.

It sounds strange to hear 'full stop' described as a leftover from telegraph technologies. To me, it's just what I call the dot at the end of a sentence.

In American English, 'period' is used in the same ways (indicating the end of a sentence and, like in the above case, to indicate that a matter is closed for further discussion).

It's the same as ending a statement with "period." As in, "We connect people. Period." said by a Facebook exec to justify their use of dark patterns. It's for emphasis.

Not only that, "period" is the American English word for the very same punctuation mark the other side of the English speaking world calls a "full stop".