Yeah, no, radio is the fastest means of long-distance communication, and interstellar radio transmissions would require massive antennae and dishes or other types of transmitters and receivers. Look at the planetwide arrays of radio telescopes used to scan for extraterrestrial signals and you’ll get a sense of the scale.
Most sci-fi authors, as far as I know, avoid that tricky detail entirely. I suppose the presumption is that if humans have colonized distant planets, then communication should be no problem. But you’re right that it is. Humans could eventually colonize the galaxy, even with current propulsion technology (given a few million years). But communications won’t move any faster than the speed of light...unless you wave your hands.
Ursula LeGuin famously invented a fictional device called an “ansible” which allowed interplanetary ambassadors to communicate with the governments on their home worlds in real time, instantaneously, with no delay in communication, despite the staggering distances between planets.
In his incredible Remembrance of Earth’s Past trilogy, Chinese sci-fi author Liu Cixin describes alien technologies that use either neutrinos or gravitational waves for rapid long distance communication. These also involved massive arrays for detecting these nearly undetectable forces. I can’t remember his explanation for why they’re superior to radio, though. Maybe longer range? Radio waves rapidly fall off with distance. Speed is always limited by the speed of light, and I remember there still being some sort of delay involved. More importantly, it sounded cool, and it was an inventive idea. Liu also describes using the sun as a sort of radio transmitter—because in his story, ground-based arrays were not sufficiently powerful to broadcast an interstellar message, even to the nearest stars.
Such a plot device can be used in many unexpected ways, given the huge time gaps between communications. Perhaps you’ll come up with your own. It all depends on how much you want to bend the laws of physics, and how much you care to either explain or omit details. There is an art to not spelling things out. Sometimes it’s best to let readers wonder.