I noticed that letterboxd was among the top pinned sites, so I thought I would check on this issue again. Looks like it has been a year!
For an apples to apples comparison I ran the exact same searches as above:
(a) "drive my car" movie 🥳
Feb 2024: letterboxd was not a result 😢
Today: letterboxd was top result 🥳
(b) "drive my car" 🤨
Feb 2024: letterboxd was not a result 😢
Today: letterboxd was first result on second page 🤨
(c) drive my car movie 🤨
Feb 2024: letterboxd was not a result 😢
Today: letterboxd was first result on second page 🤨
(d) drive my car 🥳
Feb 2024: letterboxd was first result on second page 🤨
Today: letterboxd was top result 🥳
(e) "drive my car" letterboxd 🥳
Feb 2024: letterboxd was top result 🥳
Today: letterboxd was top result 🥳
Definite improvement, despite weird ones like (c) still struggling. It makes sense to me if just the title doesn't work, but I would hope that adding 'movie' clears up the ambiguity especially as the search engine only returns results based on the movie on the first page. (As a thought, I just checked and "drive my car film" (no quotes in search prompt) leads to letterboxd as the top result!)