One thing would be interesting was to know who pushed for it to be withdrawn for now, and why.

This is trying to be a democratic process. There is no single "hero" to worship, but a number of things to consider.

The German Bundesregierung signalled a few days ago they would vote against Chatcontrol (IIRC, it is part of the Ampel coalitions founding contract to vote against surveillance enhancing measures on the EU level.) Nancy Faeser, Social Democrats, Germany's interior minister and usually not against surveillance, and Marco Buschmann, Liberal Democrats, Germany's justice minister, released statements that Chatcontrol is irreconcilable with liberal democratic states of law. The Greens were opposed anyhow and said so the last few weeks. So, unity of sorts.

France had said from the start they would vote against it (but apparently backtracking after the EU election) and with the two biggest countries in the EU against it now, the law had little chance to pass the informal council vote.

Add on top that around 30 MEPs from the Greens, Liberals and Social Democrats already wrote a letter stating that their fractions are opposed, thus ratification would have been unlikely. Add on top strong efforts by economic lobby groups, I guess the Belgian president of the council saw no reason to put the vote forward anymore.

Of course, all this could be wrong. I'm just puzzling things together I read over the last few days and weeks.

Yeah I think you're right, but it's a shame that we have to piece the puzzle together ourselves, and still don't have complete certainty. It's certainly a process where more transparency is possible, as a general point.