Choosing an appropriate constant current LED driver
Will the Mean Well driver be able to replace the current driver

Yes.
Note this meanwell driver has a Protection Earth wire which must be connected. Your original wire does not.

Can I adjust the output current to, say, 500mA and by that drive the LEDs at a lower brightness?

Yes

Will this cause the driver to output significant heat (I could not find out if it is linear).

No, dimming controls the switching converter inside. Efficiency vs load is mentioned in the datasheet. While efficiency decreases slightly at light load, it's still pretty good. At max output power, having low % losses is important. At low output power it matters less.


Assuming I wanted to add dimming functionality (e.g. through an ESP8266 and PWM, using the mean well B model). How would I limit the driver to 650mA? Is this what the AB model achieves?

Yes it'll work.
If you want the ESP8266 to be able to turn off the Meanwell supply, then ESP8266 needs its own power supply, like a USB cellphone &quot;charger&quot;. Besides powering it from 60V would be inconvenient.
Note datasheet says DO NOT connect &quot;DIM- to -V&quot;
Check if the Meanwell can turn off the LED completely. I don't think it can. So if you want this you'll probably need a relay driven from ESP8266 to switch the mains.
Dimming needs a 10V PWM though, so an ESP8266 powered from 3V3 won't achieve this.
However the Meanwell has a built-in 100μA current source pulling the DIM input up to 10V. All that's needed is a transistor driven by PWM to short the DIM input pins together. You can also use an optocoupler. When the transistor/opto is on, it shorts the DIM input. When it's off, the internal 100µA pulls it up to 10V. So all you have to do is PWM the transistor's base (or the opto LED) and here you go.