Why all of a sudden do I need an approval to send an estimate to a client?

Changes on your access role happen if your primary or company administrator updated your access rights, Yup.

I'd recommend reaching out to your them so they can adjust your access rights appropriately. Here's a references that they can use when providing access rights to user: User roles and access rights.
 

Once the client approves the estimate, you can already convert it to invoice and record their payments.

We're here to help if you need additional assistance in managing your estimates or other transactions in QuickBooks Online.