Your working hours decide when other people can book time with you, and your timezone lives with them.
Open your profile menu and choose Preferences, then Working hours under Advanced.
The page has, in order: your Timezone (Use browser timezone sets it from this device), the Weekly schedule with the days you work and their hours, and Out of office. The hours and the timezone both matter: the hours decide which slots exist, and the timezone decides what those hours mean to someone in another country.
It is the same value used to work out when you are free. Keeping it with your hours means there is one place to change when you move or travel, rather than two settings that can disagree.
If your calendar looks right but bookings arrive at strange times, check this first.
A booking link offers a slot only when both are true: it is inside your working hours, and your connected calendar shows nothing there.
That is why connecting a calendar matters as much as setting hours — without it, Atwork knows when you are willing to meet but not when you are already busy. See Connect Google Calendar.
Blocking time in your connected calendar removes it from what people can book. Focus blocks, admin time and travel are all easiest to protect that way.
For days away, add them under Out of office on the same page. Booking links stop offering those days, with no calendar event needed. See Time off and focus time.
Related: Create a booking link · Connect Google Calendar · Set your language, calendar and timezone