I like Richmond and Barnes but don’t know them well. Also like the sound of Teddington and Thames Ditton. Have discounted Kew because of the planes- are planes a significant issue in these areas too?
I live round this way but not actually in any of the places mentioned due to DP's sensitivity to plane noise (exc Thames Ditton which I don't know well enough to give a view on).
It's highly personal so v difficult to judge by other's opinions - one person's unbearable is another's don't notice.
If it might be an issue - and the fact that you're thinking about it and have discounted Kew as a result suggests it could be - and you can wait I'd honestly try to put off committing to an area until regular flights have started again, to get an idea of reality.
In the meantime you can find a lot out online about flight paths and which areas in West London are less impacted vs others (Chiswick far better than Richmond for example). You say you're in zone 2 at the moment, are you under the flight path there, for comparison purposes?
If you can't wait, at least spend a chunk of day in each location so you can experience the odd plane going over as they are now, and think - OK would this be acceptable every 3-5 minutes?
Put it this way - if I was selling a house in Richmond, I'd be making damn sure it was on the market now and not next year! Richmond is utterly lovely at the moment and it's so easy to forget how blighted it is by the flight path normally. I think there will be some very unpleasant surprises when things go back to normal for people who have moved out this way during the pandemic.