Plant cover also increases evaporation (because the water get trapped by the plants on the surface), which increases warming (because water vapour is a very powerful greenhouse gas), but also reduces local temperatures (evaporation removes heat), and increases cloud cover (which reduces warming by increasing albedo).

It's a very complex system, and working out the net effect is very difficult (as the paper says).

But wouldn't the plants and trees convert the sun's energy through photosynthesis into chemical energy? That energy conversion removes the heat.

Some, but 'removes the heat' is overly simplistic. They're not 100% efficient.