Dear Faris,
Good day! Thank you for posting your query in our community.
Based on your description, you want to revert back to horizontal tabs in OneNote.
A few days ago, a user in our forum encountered a same issue as yours, OneNote on his computer has the Vertical tabs layout which is the same as that on your new computer, and he doesn't have Tab Layout option under the View tab. He finially resolved the problem through the latest Office updates. You can refer to this thread: No option to revert back to horizontal tabs - Microsoft Community.
Given this situation, we assume the problem may be related to the specific version of OneNote. You can try to update your OneNote to the below version:
Update history for Microsoft 365 Apps (listed by date) - Office release notes | Microsoft Learn
Sincerely,
Jazlyn | Microsoft Community Moderator