If I’m using Stripe Connect, do I need to issue my users 1099-K or 1099-MISC forms?

No. If Stripe is helping your users accept payments using Stripe Connect, Stripe is the payment processor for each of those users and will issue 1099-K forms for those who meet the IRS requirements (currently, those who are US-based and have processed more than $20,000 in gross volume and 200 or more transactions in a year).