Kurtzman isn't dumb.
We may not get "Legacy" proper, but 100% we will get something Picard-Era... barring outside circumstances like P+ dying or ViaParaCBScomMount deciding the just shelve Trek altogther for awhile.
It's not a matter if "if", it's "when". It won't be for a few years. If we get anything on the sooner-side, it will be a streaming movie like Section 31. A series won't happen until either SNW or SFA are done with. This is a completely unsubstantiated "gut feeling", but I feel 5 seasons is the sweet spot in the streaming prestige TV age. So... I expect SNW to hold on another two years. If they do want to want do a PIC-era show, and they decided to drop SNW after 5 seasons, production would start after S5 wraps.
"Legacy", used in quotes as a stand-in for "PIC-Era Show", is at absolute minimum 3 years out, unless SFA crashes and burns in spectacular fashion... but I don't think it will. Even if it's not performing, I think P+ has too much invested to allow it to fail quickly, so we will get a few seasons regardless.