I don't own one of these, but I'll offer my opinion.
My first port of call is always Amazon. Amazon knows nothing about Eckman mowers. That's not a good omen.
I had a peep at the Eckman website, and am not certain which mower you are refering to. I found a 3-in-one push mower, this one:
Typically, old technology push mowers retail at about £40-£70. New technology mowers around £80-£120. As far as I can see, the Eckman push mower is old technology, and sells for £130 (although you do get the added gadgets).
You say the one you are considering is battery operated, but I couldn't see a 3-in-1 battery operated model. At least it's not described as such in the product list.
As regards aeration capabilities, if you have a waterlogged lawn, then it needs deep aeration, with a fork pushed deeply in. For the 3-in-1 push mower, the corporate website talks about "heavy clay soil can be hard and compacted". I don't personally see thay light-weight aerator making much impact into compacted heavy clay. It may work successfully as a scarifier.
My impression is that these mowers are expensive gimmicks, and I wouldn't buy them.