FWIW I took my own advice into account (sigh) so after pairing/unpairing and reconfiguring, absolutely 0 thinking, I do indeed manage to get all events properly. It’s a bit of a mess but I can get the on/off main button, increase/decrease brightness and the side buttons too (even though they somehow keep track of a value, not very convenient).
It’s been a bit tricky but seems to work reliably now!