Copy field values from Person Account to Contact & Vice Versa

Question

My org uses Person Accounts. On both Account and Contact objects i have a field TIN__c.
When creating a person account, i only populate one of those 2 fields and specifically the one on the Account. In Person Account i can use both TIN__c or TIN__pc. However, i want when creating a Person Account, to have also the information updated in the contact respectively. Also, when updating a contact's field value, i want this to be updated on the Account object.

I am thinking of introducing a record-triggered flow to handle those updates, however, i don't know how Person Accounts work "Under the hood". I am afraid that if i use a trigger or a flow on Account to update the Contact values there is a chance of going through infinite loops.

Questions:

1. Does anyone know how Person Accounts work "under the hood"? For example, when a Person Account is created, a Contact is created as well. Or, when a Contact gets updated, also the field of Person Account gets updated.
2. Has anyone had the same requirement as mine ? How did you handle it?

Answer 1

So as @identigral suggested, this is possible to be done by using a record-triggered flow. Personally, i did it in a Trigger cause i already have a before-insert one and it is a preferred way to keep one source of triggered automations in order to control the order of execution.