Consider that SameSite=Strict even breaks cross-origin links (<a> tags): if a 3rd party site links to you and a user clicks that link, the GET will be sent without cookies.
To get value out of Strict for typical sites the new pattern is to have two cookies: one is SameSite=None and allows you to do GET/HEAD/etc. requests ("read-only operations", assuming you are following those parts of the spec) and one that is SameSite=Strict and allows you to do POST/etc. ("write operations").
If https://evil.com adds a link to your site (an <a> tag) you can allow deep linking by only checking for the None cookie. The strict cookie won't be sent for <a> tags. But POSTs/form-submissions, and any page/resource you don't want to allow deep-linking for, you would check for both the cookies.
I've seen this pattern referred to as "reader and writer cookie pairs".
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This really is specifically aimed at killing CSRF attacks. It's not about tracking either way (it's orthogonal to that).