My W had a bday after BD but before she moved out, and initially I was going to ignore it but in the end it just seemed like a really cold thing to do so I did have a small party for her and got her some gifts. I didn't spend nearly as much on her gifts as I have in years past though. So it was sort of "bday lite". After she moved out we had our 20 year anniversary and gifts seemed really inappropriate for that since she had just left, so in that case I called her and asked her what she thought we should do. Her response was "I don't know, it's just all so wierd." So I said "Why don't we just go out to dinner, it's not so much to celebrate the anniversary as to just acknowledge it." And that's what we did. Then at Christmas I contacted her and told her I just wanted to verify that we were just getting stuff for the kids and not for each other, but to my surprise she DID want to exchange gifts. So then I had to do some last-minute shopping, LOL! I guess what I'm saying is try not to mind-read what you think your W wants and just ask her. Say something like "given our situation I'm not sure how to approach V Day, do you want to exchange gifts, or maybe just go out to dinner, or do nothing at all?"
Sorry, I couldn't disagree with this more. If you ask 100 married women, one of their leading complaints is that us men do way too much of the "I don't care, anywhere you want to go" thing and don't LEAD enough. And that's in HEALTHY marriages. To ask a wayward wife -- when they are actively in an affair -- what they want to do about marital things is going to come across as weak and supplicating to her. If you're DONE with her (and the marriage), and just want to co-parent civilly, that's fine but if you're still trying to DB and save your marriage these kinds of things are ATTRACTION-KILLERS.
YOU should decide what you want to do (or not do) about Valentine's Day, and then just DO it. If she asks you, "Why didn't you get me anything?" just politely and confidently say "Considering where our marriage is right now, I decided that it wasn't appropriate."
By the way, that "I decided that _____" framing can be super-useful. Not so much if you LEGITIMATELY were formerly controlling SOB in the marriage, but otherwise it shows strength. LEAD.