After installing CookieScript code, the website loading time increased

To keep the website loading time unchanged after the insertion of a cookie script, you should insert the script correctly. 

If you are inserting the script manually, make sure the script is inserted as high on the page code as possible.

If you are inserting the script via GTM, make sure you are using the "Consent Initialization" trigger to insert the CookieScript tag.

Read the guide for GTM configurations.