It's just a report. The actual blocking mechanism is enabled or disabled using Safari's Preferences > Privacy > Website tracking.
And it's only cross-site tracking it blocks. Tracking cookies associated with a particular website need to be deleted using the option just beneath it, under Manage Website Data...
If you are tempted to "block all cookies" most websites (like this one) just won't work without it. ASC uses cookies to tell Apple you remain logged in with the proper Apple ID credentials for example.
Blocking ads requires ad-blocking products, and none are completely free of side effects.
What you're experiencing is probably the unfortunate fact that there are literally no limits on the number of ads a website can host. Some of them are clogged by so many garish, attention-grabbing ads the website becomes effectively useless. That uselessness tends to become evident in older Macs running older operating systems with limited resources. Remember the outfits responsible for developing those ads work with high-end development workstations with comparatively unlimited resources, and the developers get paid according to how much attention those ads get. They don't care if that causes websites hosting those ads to load slowly or not at all.