Is it serious? Are there any actions to take following this? (I found no answer in the pill box booklet)

If you are in the third week of your pill pack and have missed a dose due to vomiting, there is no need to worry as missing a day in this week is not a cause for concern. If you have recently had unprotected sex, it is advisable to skip the placebo week and start a new pack immediately to minimize the risk of pregnancy. However, if you have not had unprotected sex, the risk of pregnancy is already low, and you can continue with the placebo week as usual. If continuing with the placebo week, start a new pack directly after completing this week. Additional measures such as taking emergency contraception are not necessary in this situation.