Is the planet growing in size?
As you say, the Earth is growing very slowly due to meteorites hitting it (in fact that’s basically how it was created in the first place) but that and comets are the only thing adding mass to the planet. Trees create mass by using the energy from sunlight to convert CO2 from the atmosphere to carbon compounds so there’s no net mass gain (mass is taken from the atmosphere and bound up in wood). They don’t convert the suns energy to mass. This doesn’t mean that the Earth may eventually pull the moon into itself though as the effect of the slight mass increase of the Earth is completely dwarfed by the tidal effect of the Earth and Moon which is actually causing the Moon’s orbit to get larger.