So... as you were quite sure about this and I had no reason to disbelieve you, I've been testing it and... yep, something's changed.
I ran the same test three times back in August 2024 and it wasn't an issue:
Fairly sure I recorded a video showing it, but it'll be on the old PS5. And, as it turns out, now superfluous.
I tested again two weeks ago (January Week 3 into January Week 4), left a gap (January Week 4 into January Week 5), and tested again this evening (January Week 5 into February Week 2... umm... yeah), and on both occasions of running the final race past midnight and picking up the final reward I couldn't pick up any rewards for the following week. In the interim week the rewards appeared as usual.
This definitely wasn't the case last summer, but it certainly looks to be an issue now.