OP, I think they've stepped into that grey area - that space where nothing has happened (yet) and one that can be explained as 'it's just a dog walk, ffs'. It makes it harder to explain your sense of unease to him as on the surface it all sounds reasonable and innocent. They will even possibly believe this themselves as it's being done so publicly. They're intentionally being self-delusional in occupying this space.
Except it's not all innocent and reasonable, is it? It's that grey area where marriage boundaries (or at least your feelings) aren't being respected. At the least, they're being sidelined. What's more, moving into that grey area allows things to more likely happen.
See, the problem with such ambiguous grey spaces is that by the time they can be seen as unambiguously shagging opportunities, it's too late. The deed will have been done.
I have had similar experiences with a partner. He was overly liking and commenting on every tweet a young female made. There was a difference of over 20 years in age between them. I raised it. The reply was 'it's just a tweet/like, etc. That's how the platform works' ('it's just a dog walk, ffs'). My response was 'Yes, but how many other 40 year olds are doing the same with this 19 year old young woman's posts?' Er ... none.
In the end, I highlighted how it could be giving the wrong impression to her, how emotionally vulnerable she presented, and that he had a responsibility, as an older person, not to encourage this. That seemed to work. It stopped.
Given your partner has already highlighted her emotional neediness as a potential issue, I wonder if you could talk to him about how she seems to be increasingly reliant on him to attend to this; that it's dodgy ground for him to walk; that, to others, it looks a tad, odd, and that you really aren't happy about the whole situation? Just let him know that people have asked you who that young woman is that he's regularly seen walking with? And that when you explain, they raise an eyebrow. Then leave it there. Hanging. Leave him to self-reflect. If he continues, do the same again, a week later.
The best scenario is where he himself comes to realise that he's acting like a stupid dick and stops of his own accord. You can't force him to stop seeing her and you wouldn't want to be cast in that role either, if not because it opens the way for him behaving in exactly the same way in future as he has no motivation to change.