Mostly yes, and the exceptions are worth knowing precisely rather than roughly, because "notes" covers a few different things.
Never shared, under any setting
What you say to an AI companion. Family can see that you chatted, if you allow even that much. Never a word of the content. A professional caregiver sees neither.
My Private Documents. Yours alone, with no switch that changes it.
These are not settings you have to find and turn off. There is nothing to turn off.
Yours unless you share them
The note you add to a check-in, a mood entry, or a vital reading. Those follow the sharing you have set for that category, so if you keep mood private the note attached to it is private too.
Notes you write before a doctor's visit are yours. What you write there for your own use is not part of what your Circle sees.
Written to be read by others
A few things are notes in name only, and are shared by design:
Messages depend on which channel you send them in. The circle channel reaches everyone in your Circle. The family-only channel reaches family members but not professional caregivers. A direct message goes to one person, and only the two of you can see it. The channel buttons near the top of Messages are how you choose.
Visit notes written by a professional caregiver. They exist so the family knows what happened, and they stay with the household.
Handoff notes between caregivers, for the same reason.
The rule of thumb
If you wrote it for yourself, it is yours. If you wrote it into a shared thread, it is shared with whoever that thread reaches. And if you are ever unsure before writing something down, open Who Can See What and check the category first.