Short answer
HubSpot's KB lists the update rules: Prefer Salesforce unless blank, Always use Salesforce, Two-way and Don't sync. Standard mappings can't be deleted, only set to Don't sync. Owner maps two-way only, with an exact match. Reference fields sync as 18-digit IDs, not labels.
1. Connected apps
Connected apps in my demo portal.

2. Pick a source of truth
Decide which system owns each field, then set its rule to match.