Newbie Gardener - Lawn & Moss Help please!

Hi everyone!!

Bought a house last August and just now learning how to garden with absoloutley zero prior experience.

I've already decided I'd like a pollinator / wildlife friendly garden and now we've started to tidy up out there, I've noticed that the lawn is in a bit of a sorry state - lots of bare patches, weeds (which I'm not too fussed about - I know the bees enjoy the dandelions and the lawn mower tends to get them anyway) and moss.

I don't know if the garden was already like this, or if it's due to the wet winter / spring but there is so. much. moss.

I was planning on using a box of miracle gro all in one for the lawn that I found in an attempt to kill some of it off before re seeding the lawn, but I've discovered there are 2 Robins (what I assume to be a nesting pair) who like to hang out in my cherry tree and just generally peruse the garden.

having done some reading, I can see that not only may the moss killer be harmful to them, which I don't want, apparantly they find the moss useful for nesting and hunting insects (which in fairness I have seen them doing a lot of!).

So my question is this:

do I leave the lawn as is, minus general mowing?

do I leave the moss, but aerate and re seed?

Is there another way of getting rid of the moss without harming the wildlife?

All suggestions welcome - I'm very eager to learn!