Hello Melissa S Lopez,
Thank you for posting to the Microsoft Community. We are happy to assist you.
In the new Outlook for Windows, you can still open attachments without downloading them by clicking on the attachment to preview it. Once the attachment is previewed, you can click on the "Open" button at the top of the preview pane to open it in its specific app. If you want to save the attachment to a specific folder, you can click on the "Save As" button next to the "Open" button and choose the location where you want to save the attachment. I have tested it on my side and I have this feature as shown in the attached screenshot. Please let me know if I got you wrong
The feature for moving attachments from an email to a different folder is not yet available in the new Outlook.
In the meantime, we sincerely recommend you post your concern as an idea to our Outlook in-app feedback site Contact support and provide feedback within the new Outlook for Windows - Microsoft Support

Our Product Development Team is committed to enhancing the customer experience by continually examining suggestions to include in the design and development of future product upgrades based on your suggestions. Hopefully, your suggestion will help many users in the future.
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Simbarashe | Microsoft Community Moderator