Dear Nebu Thomas Mathew,
Good day! Thank you for posting to Microsoft Community. We are happy to help you.
As per your description, it seems that you are having issue opening files via Office web app in SharePoint, getting auto saved and is showing as modified under your name even though I haven't made any changes. Given this, you are willing to disable auto save in browser only.
If the understanding above is right, we're afraid that there's no out of box way to disable auto save in browser only for now.
For your reference: FAQ - Can auto-save be disabled in Office for the web? | Microsoft Learn
Meanwhile, as per the test on our side, opening the file directly in browser and close without modification will not get auto-saved and change the Modified column as shown below in SharePoint.
Given this, we'd recommend you enable versioning settings in SharePoint as a workaround. Please also check if open the file in Preview mode can help.
For your reference: Versioning in SharePoint | Microsoft Learn
Meanwhile, we completely agree with you, this is indeed a good addition to the current experience in Office web app. It would be definitely ideal if we could disable auto save accordingly. We'd sincerely share your valuable feedback in Excel Feedback Community. Please also consider voting for the similar request shared below, your votes will increase the awareness coming from the product team.
The Product Team is in-charge of the feedback site, and they are constantly checking the comments and feedback from our customer. Many features have been developed or improved based on users' comment.
If the understanding above is not consistent with yours, please feel free to post back and point that.
Your understanding and patience will be highly appreciated. We hope that you are keeping safe and well!
Thanks for your cooperation.
Sincerely,
Rhoda | Microsoft Community Moderator