Thanks for coming back and playing it again, that is genuinely useful.
Glad the car colour landed. That change came directly from your first comment. The car used to take its colour from the biome so it stayed visible against every palette, which worked for finding it and failed completely at recognising it. It is now a fixed cyan and the biome only tints the rim.
The drifting did change, and quite a lot, so you were not imagining it. The old version rotated the car around its own centre, which is a pirouette rather than a drift. It now pivots nearer the front axle so the rear steps out, and the angle builds over a fifth of a second rather than snapping. The old one was flicking sides about 55 times a minute, which read as a wobble.
Worth a go on a phone if you get the chance, it is a different thing with a thumb on each side of the screen.
You have found a real gap and I am glad you pushed on it. There is no way back to the title screen once a run has started. Not a hidden key, it simply does not exist. Reloading the page is the only route, which is not an answer.
So the scores, the car unlocks and the countdown to tomorrow's track are all sitting on a screen you cannot get back to. That is going on the list.
On the framework: there isn't one. It is a single HTML file, hand written, Canvas 2D, no libraries and no build step. Nothing is fetched while you play except the music. That was a constraint rather than a flourish, since the audience is kids on locked down school Chromebooks where anything with a download or a login is a dead end.
The level of the week idea sounds right for your game. The daily works here because the track is generated, so there is nothing to author and everyone gets the same road for free. If yours are hand built then a week or a month is the honest interval, and a longer window gives people time to actually grind a score rather than just have a go.
Good luck with the web release.!!