The onus is on you to make sure the car is booked in to get its service on time.
Some manufacturers will also contact you, or the car or App may make you aware too.
I think Peugeots have a service indicator reminder, so it may be the case that the service is not due for more than 28 days.
If you require a courtesy car while yours is in for the day, it’s a good idea to book it in early anyway, as these are often in high demand.
2024 - BMW i4 Grand Coupe eDrive 35 Sport
2020 - Volvo XC40 T4 Inscription
2017 - Audi Q3 TFSi Sport S-Tronic