We both have Microsoft 365 Business Standard and M365 Business Basic subscription.
Users that are using M365 Business Standard have Microsoft Editor in Word on the Web, but all users that are using Business Basic does not have this option. I tried to provision a new user with M365 Business Standard, and the Editor showed up immediately so I know that this is not an issue with propagation. However, I'm not able to see any documentation that this is not available for Business Basic subscription.
Business Standard users
Business Basic users
Based on what I see, it should be available for Business Basic. Word for the web
Editor is included in Word for the web. Sign in with your Microsoft account for free to get basic spelling and grammar checking. Or sign in with your Microsoft 365 account to get refinements beyond the basics, including readability statistics.
Customers who sign in with an Microsoft 365 account should see Editor right away. It will take a few weeks for Editor to roll out to all user accounts.