Russia intentionally timed the killing of Navalny to happen AFTER Tucker’s interview and Moscow travelogue, not before.
Along those lines, I suspect that Navalny’s murder was a sure thing before Carlson came knocking. Had Navalny just been murdered, there is no way the interview would have happened, so the interview had to go first. Once it bore no fruit, there was no reason for delay.
An alternative possibility is that some in Putin’s faction were displeased with Putin’s nice guy act, and killed Navalny to derail potential for a negotiated settlement over Ukraine.