This is bad news for me. I am working on a simliar project (gaussian splatting + dynamic scene). Our method is different with the mentioned 4D gaussian splatting, but I am unsure shall I continue or not.
There's nothing wrong with concurrently developing something similar. I can almost guarantee there will be something different enough about what you've developed to be considered novel (if you care about publication). If you don't care about publication, then definitely keep going! Hell people are still argue about which implementation of complete specifications are the best (for good reason).
Because of the sunk cost fallacy which is a fallacy only if you ignore the emotions and trauma of having to abandon work you identify with or is responsible for your self esteem.
Don't see how the sunk cost has anything to do with it, OP clearly hoped to be first, as being first would almost guarantee a payoff of some form.
Coming out with a method second is much less likely to be rewarded by the community: not being rewarded for work completed is not sunk cost, its just a straight up loss.