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First of all, you are reading the documentation for a deprecated API. With this API you actually had two separate APIs, one from OneDrive personal and one for OneDrive for Business. For the former you'd create an OAuth2 application on Windows Live which would be common for all users (that's what we did) and they'd only be able to access their OneDrive personal drives — not even their personal drives provided by a school or organization.

The other option was to create an OAuth2 application for a specific Azure tenant. This was absurdly complicated, it had to be done separately for each organisation and would only give access to that organisation's drives (and only according to the privileges delegated to the OAuth2 application). We never implemented that because it would require EITHER creating a separate integration for each and every client of ours (we'd have to charge an upfront  itnegration fee and a yearly maintenance fee on top of the subscription for that to make business sense) OR you'd have to figure out how to create the app in Azure and how to set up the endpoint mediator on your site. Both options require extensive, very expensive support. We can't do that with our current prices, it doesn't make sense to charge everyone extra to subsidise a niche use case and it's impossible to sell a product where a certain feature requires an additional payment that's 10 to 20 times bigger than the product's subscription fee. What made most business sense is refuse to implement this feature and possibly lose a dozen or so clients.

This all became moot in 2019 when Microsoft FINALLY deprecated the kludgy OneDrive API and replaced it with the Microsoft Graph API (https://docs.microsoft.com/en-us/graph/use-the-api), a unified API for all of its services. Its OneDrive integration is here:https://docs.microsoft.com/en-us/graph/onedrive-concept-overview. According to Microsoft, it lets you upload to any of the drives you have upload access, no matter if they are personal or business (organization) drives. The default drive you have access to is your personal drive and that's what we use in our integration. Remember, the original goal was to let people use their Drives regardless of whether they were OneDrive personal (part of their personal account or personal Microsoft Office 365 or-whatever-the-call-it-this-month subscription) or OneDrive for Business (part of their school/organisation's Microsoft whatever-they-call-it-this-month subscription). So, this part works.

What you ask is a bit different. You want to write not to your personal drive provided by your organization but to a different drive which you have write access to as part of your organisation group. Writing to a different drive directly requires some missing plumbing. The only way around that that would work with what you are looking for is possibly doing the same thing we're doing with Google Drive. After you copy your tokens we can access the /me/drives endpoint to get the IDs of the drives you have access to and let you select which one. I can give it a go but since I don't have a business drive and don't have a spare domain to run a new MS subscription I won't be able to test it. I will work on it today. Tomorrow I'll be making releases and you can try that (tentative) feature.

Go to the Configuration page of your backup profile.

Authenticate to OneDrive using your business account.

Click on Save at the top of the page; the page reloads.

Wait for 5–10 seconds.

Look at the OneDrive configuration. There's a Drive drop-down. It is populated by the drives the OneDrive API says that you have access to. Select which one you want. Click on Save & Close again.

If you have two options it means that Akeeba Backup was able to successfully communicated with the OneDrive API and the OneDrive API responded that you only have access to one drive.

The first option in that list is a built-in option which really is “we have selected no drive” and the OneDrive API understands to mean as “use the default drive for the account” during upload — that's how it worked before.

The second etc options are those directly returned by the OneDrive API.

Unfortunately, delegated access (what you are using) does not set up a Drive. It sets up a special folder in your drive. You cannot access these folders using Akeeba Backup. This would require a different connector, one I can neither develop nor test as I don't have a subscription to their most expensive tier which allows this access, nor does it make sense to purchase that for a feature that has only be requested once in 8 years by just the one person, you. 

If it's possible to create a new Drive and share it with your backup then Akeeba Backup will have access to it and you will be able to write to it. Unfortunately that's the full extent of advice I can give as I don't have access to these features.