Depending on your software, you can! I know Google Calendar allows you to restrict shared calendars to just time ranges, it'll show up as "not available".
Settings > Calendar Settings > Access Permissions > Make Available to Public > on the dropdown, pick "See only free/busy". Now you can share the link with your work calendar and it'll show up as indistinct blocks of time.
You can do it both ways, and you'll be able to check your availability for both work-related things and personal things in their own calendar, but contextualized.
Even my work calendar doesn't share the details of what I'm doing in a busy slot. Not particularly something anyone needs to know. If someone really needs to meet and my calendar looks blocked they can ping me to see if there's anything I can drop or move. It's not really up to them to make the decision (unless I work for them and it's urgent).
Settings > Calendar Settings > Access Permissions > Make Available to Public > on the dropdown, pick "See only free/busy". Now you can share the link with your work calendar and it'll show up as indistinct blocks of time.
You can do it both ways, and you'll be able to check your availability for both work-related things and personal things in their own calendar, but contextualized.