I would put the odds of a mid-season extension at basically zero, or at least act that way for the purposes of any deal. To that end, here's the case you could make:
Ohtani is the high end arm *and* bat the Cubs are currently missing. They have the current SP depth to go to the 6 man rotation Ohtani requires, and they have a mostly empty DH slot for him to have maximum impact(if Mancini starts hitting this is less relevant but only a little). Let's put this another way, if the Cubs were in contention at the deadline and traded for Rafael Devers AND Corbin Burnes, what would their championship odds look like? I'd argue they'd look as good as most teams. Even without the extension, Ohtani is buying a serious chance at a championship and that's very much something.
The question then becomes at what cost, and that's where recent trends make this more viable. Ohtani might be the unicorn that breaks the scale here, but we've seen numerous examples in recent years that rentals are not bringing tippy top prospects in return. They're bringing fringe top 100 guys or players on the upswing who may get top 100 hype after the current season. In other words, the exact meat of the Cubs prospect depth, which for the serious chance at a championship(and possible future benefits) could be worth parting with 2-3 guys of that caliber.
As for those future benefits, if you're the Cubs and you are interested in signing Ohtani, there's several benefits to having him in the org. An Ohtani-led Cubs are going to be playing in front of big crowds and almost certainly meaningful postseason baseball, considering how important winning is likely to be to Ohtani in choosing a future home it would go a long way to wipe out any current view of the Cubs as non-contenders. It also gives him an up close look at the things the Cubs have been pretty good at selling already, their pitching development, clubhouse environment(complete with existing Japanese star signed for 3 more years), etc. It also lowers the uncertainty for the front office in offering absurd money to a player who they haven't gotten an up close look at and how they can help him maintain success or (somehow) find another level.