how do I know if I have 365 E3 or E5

If the subscription is Microsoft 365 Personal, that is not Microsoft 365 E3 or E5.

E3 and E5 are business/enterprise plans. Microsoft 365 Personal is a home subscription.

For a home subscription:

• Free at Microsoft365.com means no active Microsoft 365 Family or Personal subscription.
• Subscribed means an active Microsoft 365 Family or Personal subscription.

If checking a work or school account, the license can be verified in the Microsoft 365 admin experience:

1. Sign in to admin.microsoft.com with the work or school account.
2. Go to Settings > My app settings > Office 365.
3. On My account, select Subscriptions.
4. The assigned services and license appear there.

For the OneDrive concern: the context only states that if OneDrive is needed for commercial use or greater sharing controls inside or outside an organization, that requires OneDrive for work or school. It also states there are separate Microsoft 365 plans for businesses, enterprises, schools, and non-profits.

References:

• What's the difference between a Microsoft 365 subscription and free web apps
• Troubleshoot installing Office
• Which OneDrive app?
• What's the difference between a paid Microsoft 365 subscription and the free web apps?