Ordinary switches require only "always-hot" (from supply) and "switched hot" (to the lamp). They do not need neutral. Because of that, many older switch circuits are wired only with always-hot and switched-hot.

There are many switches which do an extra trick - lighted switch, dimmer, motion sensor, smart switch, timer, you name it. They need to power themselves. How? The newer ones attach to always-hot and neutral, getting power the normal way. However many such devices are made to be compatible with old switch wiring.

As it happens, incandescent bulbs are electrically pretty much a dead short when they are off. These powered switches can simply leak current from always hot, through themselves, to switched hot - and the incandescent light will not light enough to be visible. However, LEDs are so efficient that this small current makes them light up slightly.

Your "regular single pole switch" wasn't. It was a lighted switch or some other powered device. That's why it leaked a little bit of power through the LEDs. When you switched to a dimmer, you went out of the frying pan into another frying pan, because again you had a switch that leaked power through the LED.

You need to use powered switches (such as dimmers) that attach to the neutral wire. They will not leak current through the LEDs, and that will quiet them.

Another option is to put a module in parallel with the LEDs that is designed to leak the current that the switch requires, such as Lutron's LUT-MLC module.