Now, anyone can click on my user name and see all my posts on all my sites.
If I delete my accounts on, say, 2 sites, will they still be linked in that way? Or will those deleted accounts look like they belong to 2 completely independent users?
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The accounts will be gone. There is not going to be any indication they were linked.
Any posts from those accounts will have a grey user card with the now-defunct user id on them, with no link to an account.
It is theoretically possible for someone to link the user id to your other accounts if they look at archived copies of Stack Exchange pages. The Internet Archive could include copies of the page with a username on it, or contain one of your other account listing your connected accounts, and by looking at the URL you could confirm it is the same user id. This requires luck and considerable sleuthing however.