Your thought process here seems to be that GT7 will have Sport Mode, PD won't want to drop the 8m+ userbase it has on PS4, so GTS and GT7 will run merged events (at least initially) courtesy of BC and Crossgen, and that means the two must play in an identical way or one console's users will have an unfair advantage.
That's fine - it makes sense, to a point - but it's not directly related to the existence of a GT Sport Live icon in the main navigation screen or anything else we've seen in the trailer. In addition, one thing I've learned over the last 20 years is that what PD does it not always entirely based on what makes sense (at least externally; we keep on buying the games though).
GT Sport's median active weekly userbase is around 140,000 players, and has never exceeded 275,000 players. Kazunori's presentation in Paris in 2019 said that 348,000 people raced in the FIA events across all of 2018 (and some of those were second (and third) accounts!). When you take into consideration the prospect that GT7 could ship 3m copies in week one (GT5 sold 5.5m in its first two weeks), there's more than enough people to pack out the Daily Race and FIA lobbies.
If we assume it's a launch (and if it is, bundle) title and that GT7 follows GTS's path and doesn't start the FIA competition in earnest until Spring, that's five months to build up a playerbase - by which time GT7 could have exceeded GTS's lifetime sales (it may not do so, but a "proper" GT game is more likely to see GT3/4/5/6 sales rates than GTS sales rates).
We should also take different kinds of sport mode races into account. It is absolutely possible that GT7 and GTS will run merged Daily Races with similar underlying physics - and we'll have threads just like wheel vs. controller on PS4 vs PS5, and the advantage each confers - but only run FIA events on the new game and console. There isn't any particular reason why this couldn't or wouldn't happen.
This is, of course, all conjecture. That's why I'm presenting it as such. The only plain fact we have about online multiplayer is that we've seen nothing of any online multiplayer in GT7 yet. In terms of actual driving, all we've seen is an offline race at the rejigged Trial Mountain with (presumably numbnuts) AI opponents.