Does Family Sharing cost me anything?

No the family sharing itself costs nothing

But If you turn on purchase sharing and some family members purchase using your payment method you will pay for that purchase.

Share App Store, iTunes Store, and Apple Books purchases with Family Sharing - Apple Support

There is no charge for Family Sharing of Apple TV+. See the following from Get Apple TV+ - Apple Support

If you join Apple TV+ or start a trial and you use Family Sharing, you and up to 5 other family members get access to Apple TV+.