Hi Oliver,
Thank you for the post, we are glad to help you.
For your concern, your thought was right regarding the sending limits of 10,000 per day. In addition, the maximum number of recipients you could send for a single email message is 500, so you can’t send 10,001 emails for one time.
You could refer to this document for more information.
In terms of up the limits of recipients:
For the administrator: You could create and use distribution groups at the exchange admin center, the distribution group that is stored in the organization's shared address book counts as one recipient, which will increase your limits of recipients.
note: if some of the recipients are external users, you can’t add them to distribution group directly. you can involve your administrator to create mail user/ mail contacts for those external users to your organization
If you have any other further updates, let us know please.
Kind Regards,
George