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Hi Chloe,
Good day to you!
I hope you are doing well. Thanks for reaching out to our Microsoft Community Forum. We will be happy to help you.
Regarding "My email address for the later account appears to be my email with @ changed to _ and adding “#EXT#@[servername].onmicrosoft.com” at the end", this is normal behavior after the tenant admin has added your account as a gust. Generally, in this case, if B2B collaboration is configured correctly, you can log in with your personal email address and do not need to use the account with "#EXT#@[servername].onmicrosoft.com"
Regarding your question, after adding you as a guest user, the tenant admin can add your account as a member of this group. The tenant admin can go to the Microsoft 365 admin center> Teams & groups> Active team & groups> select the relevant group> Membership> Members> Add members. As shown in the image, I added the OUTLOOK personal account as a group member (having already added the account as a guest). Later, you should be able to open the online files in the Office desktop apps (Office for Windows or Office for Mac).
Regarding "the only way for me to access the newer account is with an authentication code send to my emails", it seems that you are authenticating via One Time Passcode experience. Microsoft provides one time passcode experience and Microsoft Entra B2B for external collaboration. In this case, you need to contact the tenant admin to check the relevant settings in this tenant.
For your reference:
Secure external sharing recipient experience
SharePoint and OneDrive integration with Microsoft Entra B2B
Overview: B2B collaboration with external guests for your workforce
Regarding "Would there be any way of me accessing this account through the OneDrive mobile application", to my knowledge, this is a known limitation for guest users (external users). Guest users can view or edit files using the Office desktop apps, and they can sync SharePoint folders/libraries to their devices using the OneDrive desktop apps. However, there is no way to access them through the mobile apps.
When you have any updates or concerns, please feel free and come back to share them with us. We will continue to help you.😊
Sincerely,
George| Microsoft Community Moderator