Former flame has moved on - appropriate to message an apology anyway?

There was a girl that I had a casual fling with over a number of months. Now when I say casual fling, I mean that we slept together probably 5 times, over the course of 5-6 months. So in the scheme of things, that might not sound like THAT much, but still spoke semi-regularly etc. Lovely girl, we got on great, and there was no malice on either end, but I was somewhat emotionally unavailable.

In short, my Mums been quite unwell the last 6 months, and it was occupying so much of my time, that it just made me feel like I didn't have the emotional capacity for something serious, which I had told her and was relatively upfront with her about that.

Recently though, I noticed that she's began dating someone else. And, out of nowhere, it really affected me, and made me think about what could have been.

It made me think about how I treated her. There was never any malice whatsoever, but a real lack of effort on my behalf. Very slow to initiate any plans, sometimes very slow reply times (she’d do the same sometimes, but still, it’s not great), and just a general lack of effort from my end. Sometimes I question whether she felt a bit stronger than I did though, so I feel bad about it.

Anyway, I’m wondering whether it’s worth sending her an apology text, just saying how sorry I am for my lack of effort, saying how it was such a bad personal year for me, and I didn’t know how to handle things externally a large amount of the time, hope there’s no hard feelings etc.

Would this be appropriate to send, even if she does have a new partner now? Clearly I didn’t put in enough effort, and didn’t have strong enough feelings for her to do so at the time. But now I’m a bit upset at myself, but also feel a large sense of guilt if I behaved in a fairly poor way.

Advice would be great. Thanks