I think the clots from contraceptive pills that you refer to are considerably less deadly than CVST. I don't know how the numbers stack up, I suppose indeed contraceptives are more dangerous than this vaccine anyway. But in any case, you're doing an apples-to-oranges comparison.
Contraceptive pills are taken by millions of women, of course, but there is a large proportion of women (possibly a majority) that do not want to take them. Alternatives like the condom, IUD, sterilization, etc. are widespread even if they are more uncomfortable, precisely due to the pill's side effects. And no one (or no one in their right mind, at least) questions a woman's decision to not take the pill.
Here we are talking about a vaccine that your health system actively calls you to take in the context of a campaign, no alternatives are given (in the words of a politician in my country, "vaccines are not yoghurts, you cannot pick your favorite flavor"), and while you are free to refuse it, you are then called an antivaxxer, and not given any guarantees about being able to take another in the future.
The standards really cannot be the same for something that you take at your own risk among tens of alternatives versus something that you are pressured to take without even a clear guarantee of alternatives. And you cannot use contraceptive pills as a metaphor for something that people just take willy-nilly without a second thought, because plenty of women definitely don't do that.