Thanks!
I prefer setting everything up in config files, and found in your topic how to add metadata to an item, so item config now has stateDescription=""[min="0", max="100"] added to it:
Dimmer EntryLightColor "Színhőmérséklet" <light> (gEntryLight) ["Light"] { channel="mqtt:topic:entry:colortemp", autoupdate="false", stateDescription=""[min="0", max="100"] }
which resulted in changing into 0-100 range, with the slider dot at correct position:
I’d still rather have the range left in 153-500 as it was before (and somehow have the transformation done between that and 0-100), but the the point is now it reflects the state of the lamps colour temperature correctly, and most importantly, changing the slider creates MQTT message, so it finally works!