Think I [30M] have misinterpreted some signs from a female coworker [40F] and made them uncomfortable – how do I rescue the situation and ice things down ethically?

TL;DR: I thought my coworker was flirting with me so I flirted back. It now looks like I misinterpreted. How do I get out of this situation, avoid a disaster while sparing their feelings?

I’d be grateful for a some takes on this –

A coworker at my job, a supervisor on another team, has been very friendly since joining. Our chats have quickly moved off work and into our private lives where it turns out we have a lot in common and quite early on she invited me to hang out outside of work in the context of a shared interest of ours – comedy shows – fixing up a meet up on two for a few months time.

Since then we’ve also started playing some online games together – another shared hobby – and they made a few remarks that I, at the time, interpreted as indicating a deeper interest than just friendship. They asked me if I wanted to rent from them, asked for my number and then very quickly afterwards asked me about my age in a way that seemed like they were thinking about possible romantic compatibility. When I guessed they were younger than they are they responded with something like ‘it’s sweet of you to pretend I look so much younger’ and they’ve said other things like that which have built up this impression that this might not just be a friends thing.

Anyway, we’ve been chatting for a while now and I’ve gradually started flirting a bit back. I haven’t said anything flatly outrageous but I have thrown a few more compliments at them and probably overshared and a few days ago asked them to meet up for another event earlier than planned. Well, this does not seem to have gone down well. They’ve gone noticeably cold and seem to be disengaging. This has made me concerned about what this means in the context of work. I don’t think I’ve crossed any hard lines or done anything outrageous but I do worry I might have made them uncomfortable. I’d like to cut the cord on the relationship before things get any worse – the risk of something going wrong or being misinterpreted either way is just too great for me. I want to ice off the relationship and withdraw myself but I’d like to do this in an ethical way that won’t hurt their feelings.

How do I do this? I’m leaning towards just stopping replying to them and letting things peter out on their own? If you were the woman in this situation would that be your preferred outcome?

I’m concerned about their feelings and also of course protecting myself. The sudden change in tone has thrown me a bit and I’m looking at some of my flirty comments now and thinking I’ve badly miscalculated.