Part of macOS
biomedActivity history
○ Leave it
Keeps a private record of activity for suggestions and Screen Time.
What it is
Stores on-device history that features like suggestions and Screen Time use.
If you stop it
macOS starts it again straight away. Leave it.
The verdict
○ Leave it. Part of macOS, or something that starts again by itself. You never need to close these.
In Activity Monitor
biomedBiomeAgentbiomesyncd
From Procession’s guide, in the words the app shows.