Tap into Intention Repeater Anywhere?

The Holo-Stones don't actually reference the Repeater.
They are actual ethereal energy forms, millions of them,
all over the globe, in a geometric configuration.

The Repeater uses a black hole Servitor.

You can talk to the HR6819 Servitor if you want to use the Repeater Servitor.

Or the Holo-Stone Field if you want to talk to the Holo-Stones.

In answer to your question about why Repeater requires more than once, well
if you talk to it you can say something once and it will work.
But Repeating intentions is always more powerful.

You can Repeat with Holo-Stones too with your voice,
just not Repeater the Stones that rapidly cause they seem to feel hot to you.