I had a neighbour just like her! Other neighbours thought she had a mild form of dementia - or possibly a personality disorder. She felt compelled to monitor the whole street, carefully watching anyone outside - and commenting.
I, too, built an arbour, as garden buildings can be 2.5 metres tall (in the UK) whereas fences can only be two metres.
I made a huge effort to be outwardly friendly and cheerful at all times. To avoid any interaction, I'd appear to be busy, just smile and wave, while wearing headphones. (No, I wasn't listening to music, just pretending to.)
If she insisted on talking, I'd cut it short, saying 'I'm cooking, must go in and check' or 'My daughter's phoning soon' or 'I'm just on my way out' etc. - any excuse, in fact.
I think she was very bored and/or jealous - oh, and trying to provoke a reaction with her petty complaints. I'd still smile and just say 'It's fine, it's OK, just a bit of noise while I mow the lawn, nothing to worry about', so be dismissive in a happy sort of way.