Hey bharatcrs,
We totally understand if you would not like to add the mail account directly to your Mac for concerns of storage limitations.
We recommend clearing out your browsing history as well as your caches and cookies in both browsers as this will reset the amount of activity that was previously stored.
To clear out the browsing history for the Mac, check out this resource: Clear your browsing history in Safari on Mac
To clear out the cache as well in your Safari browser, follow these steps: Open Safari > Choose Develop in Safari menu > Empty Caches
If you still have Chrome downloaded on your Mac and would like to complete this troubleshooting there as well, check out these resources:
Clear browsing history in Chrome: Clear browsing data
Clearing out cookies and caches in Chrome: Clear, enable, and manage cookies in Chrome
Once you have cleared out this information, you should hopefully see a difference in the CPU percentage in Activity Monitor on your Mac.
Best wishes.