>Even humanity’s (weak) radio emissions would be detectable from tens of light years away, and stronger emissions from much further.
That's not true. Non-directional radio transmissions (e.g. TV, broadcast radio) would not be distinguishable from cosmic background radiation at more than a light year or two away [0]. Highly directional radio emissions (e.g. Arecibo message) an order of magnitude more powerful than the strongest transmitters on Earth would only be visible at approximately 1000 light years away [1], and would only be perceptible if the detector were perfectly aligned with the transmission at the exact time it arrived.
That's not true. Non-directional radio transmissions (e.g. TV, broadcast radio) would not be distinguishable from cosmic background radiation at more than a light year or two away [0]. Highly directional radio emissions (e.g. Arecibo message) an order of magnitude more powerful than the strongest transmitters on Earth would only be visible at approximately 1000 light years away [1], and would only be perceptible if the detector were perfectly aligned with the transmission at the exact time it arrived.
[0] https://physics.stackexchange.com/a/245562
[1] https://arxiv.org/pdf/astro-ph/0610377.pdf