HSAs are available only with compatible high-deductible health plans. If you switch to a non-HSA compatible plan, you'll no longer be eligible to contribute to your HSA. Your existing HSA funds are yours to keep, so you'll still be able to use the funds in your HSA after you switch medical plans.
If your account is with WealthCare Saver, you can continue to use your Zenefits card to access the remainder of your funds.
You will still see the Health Savings Account app on your dashboard.