This is a photo of the pink spots:
There is no discoloration of leaves as far as I can see.
The plant itself
What are they? Are they harmful? If they should be dealt with, what is the most eco-friendly way?
It is probably Pink Wax Scale insect, they're the right shape, though the colour varies from greyish pink to pink; this infestation is not uncommon on Lilly Pilly. I've never seen them quite such a glorious shade of lilac pink before though,they look quite pretty; you may see lots of ants crawling on the tree, which would confirm it is scale -they like the honeydew the scale produces. Given the size of the tree, it will be difficult to do much about the infestation - the usual course of action is to pick or rub off what you can with a cloth dipped in alcohol or methylated spirits from the woodier parts, and using an oil spray to try to kill the crawlers, see here under Pink Wax Scale https://www.gardensonline.com.au/gardenshed/gardendoctor/pagenumber_6.aspx
You and your tree may just have to live with the infestation I'm afraid, as the plant is so mature and large. Severely affected branches can be cut out if they start to look sick.
It's a gall caused by a parasitic wasp. In most cases there isn't much to be done about them, though you may be able to set traps for the adult wasps. In general unless the tree is already suffering stress or disease, they will not really cause problems for the tree.
www.nature-and-garden.com/gardening/gall-wasp.html/amp
Edit: Bamboo is correct; pink wax scale insect is the correct answer.