FR207 diode datasheet calls them (FR107,207,307) "fast recovery" but not really. It's a bit slow, rated 500nsec recovery. Higher voltage diodes are also slower. FR207 is 1,000V which is not needed at all. 1A should be enought for the charger control and LM358.
We don't know the charger's frequency, but I find a slow rectifier with no snubber will run hot and even fail, despite the load being small.
I would upgrade to a faster recovery diode with lower voltage, under 400V. Like UF4004 (50nsec) or
BYV38-200 (30nsec) etc.
A mistake I have made is thinking the diode failure is due to current, so I upsize the diode but it's worse because bigger diodes are typically slower. FR307 is still 500nsec. slow.
The charger might have a design problem with spikes/ringing coming out of the transformer, if there is no snubber network across the secondary-side rectifier diodes. Or the primary snubber is inadequate.