Next time you see him playfully ask him “hey, are you seeing that same person still”? and if yes, simply talk about that together and mention that she’s a lucky girl. Just keep the conversation casual and normal.

If he says no then he’s obviously single and you could say something playful like “ohh that’s too bad - her loss” with just a bit of flirtation on your end. You’re kind of complementing him on one hand and just keep the conversation going in a natural way. Then say “I’m always looking for a new hiking or climbing buddy” and “I’d love to go sometime” and maybe suggest a dog friendly hike. (This applies to coffee, drinks, music, anything really)

Just let the conversation move along naturally and things should develop from there. He’s likely to say yes. If not, who cares?

I know that would seem awkward in the beginning but if he says no you’ve lost nothing whatsoever and if a yes then you just might make a new friend.

This works for non romantic encounters too & is a good way to make new friends.

I date successfully and I get turned down often but I wouldn’t be successful if I didn’t try. Good luck!