Damp lawn turf with clay underneath

I live in a new build it’s only 4 months old. The turf in the garden has been put on to of clay. I’ve worked heard and reseqrched to make sure I look after it correctly. It was looking amazing! Thick healthy grass for months! Now we’ve had a lot of rainy days and the last week or two loads of mushrooms and patches are starting to turn yellow. Also noticed what I think are fungus gnats and similar.

Can I aerate it with a roller aerator without damaging the grass and roots? It’s too wet to mow at the moment even on the highest setting

Any advice welcome!