Not directly related to leap year, but a couple weeks ago I set up a script for testing notification behavior that used libfaketime to simulate runs at different times.
I guess this might be less-trivial if you've got a distributed multi-service architecture and perhaps also depend on APIs that aren't under your control in the first place.
Set up a backdated timeserver and use that to sync time
That's generally risky to do nowadays because of things like TLS certificate expiration.
In a few hours you'll be able to backdate to "yesterday", with very low chances of hitting cert expiry issues (but I wouldn't be surprised if OP's issue involves components outside of their control or ability to test end-to-end)
I should have written something along the lines of "validity date ranges" instead of expiration: you're much more likely to run into problems where you run into a certificate that was issued in the future relative to when you think is now.