Considering Picard is likely to be in a schedule now where its seasons will come out earlier than Discovery's for the forseeable future (i.e., Season 1 done before Season 3 of DIS, and likely Season 2 beginning production before Season 4 of DIS) you're likely right so long as Discovery gets a fifth season it will go off the air later.
That said, If Picard is a smash hit (as far as streaming shows go) I could see them going with a continuation in all but name for the "fourth season." Basically Stewart exits, and the "new cast" soldiers on - possibly with someone who is relatively young from Berman Trek and bankable (like say Jeri Ryan) as the new lead. Indeed, I wouldn't be surprised if Jeri was brought into the show for that very reason. Seven didn't have any within-show connection to Jean Luc, but if the overall arc of the show is Borg focused, she would be a natural replacement as lead if Stewart's health fails.
Of course, Section 31 is going to be a Discovery spin off of sorts, as will Pike-Trek if it arrives, meaning Discovery will have "won" this competition anyway.
I don't view it as a competition. If I didn't think DSC would be around much passed the third season, I'd say so. I think it will run four seasons minimum. From a hypothetical fifth season on, it's anyone's guess. I'm totally clueless about what Star Trek in general might do with the 32nd Century once
Discovery opens up that Pandora Box and how they will or won't continue with it.
I think
Section 31 is the one most likely to be cancelled if it doesn't go over well, because of how unconventional it will be and because intensity against the concept by some is stronger here than for anything else.
With
Picard, you're probably right. Something else will be spun off it.
The Pike we'd see in a Pike Series would be the one from
Discovery but there are people who'd rather have a Pike Series than
Discovery (as we both know), so whether or not Team Pike is the same as Team Disco is debatable, even though there's a lot of overlap. You'd have the Pro-DSC Pike Fans, the Anti-DSC Pike Fans, and the Neutral-DSC Pike Fans. I don't think a full-on series is where they're going to go with
Pike, though. I think a Pike Series wasn't part of their plan and they were caught off-guard. And Anson Mount doesn't want to do a full series, I don't think. So I'm imagining either mini-series with him or TV Movies.
I don't know how CBSAA will handle
Lower Decks over the long term, as it's an animated series -- even though it's intended for adults -- but if we look at just the live-action material, that's
Discovery,
Picard,
Section 31, and if you through
Pike into the mix, that's a full year of live-action Star Trek. You might be able to get away with
Lower Decks airing at the same time as a live-action Star Trek as it's an animated series and some people just won't watch a "cartoon".
I think most of these series will
not run seven seasons.
They clearly want to do a
Starfleet Academy series too. And no way would that be able to be slotted in if they wanted to do one live-action series at a time. But I do think they might hold off on
Starfleet Academy until they can get some kids roped in with the Nickelodeon Series. Once they have more younger fans, that's the time to unleash
Starfleet Academy. As it is, this is one of the few places where 40 makes me feel young.
That post went longer than I intended. Anyway, that's my estimation of where all the series stand.