I find that cookie setting really confusing. It means that cookies will only be respected on requests that originated on the site that set them... but that includes when you click links from one site to another.
So if you follow a link (e.g. from a Google search) to a site that uses SameSite=Strict cookies you will be treated as logged out on the first page that you see! You won't see your logged in state until you refresh that page.
I guess maybe it's for sites that are so SPA-pilled that even the login state isn't displayed until a fetch() request has fired somewhere?
SameSite=Strict is belt-and-suspenders protection in the case where you could have GET requests that have some kind of impact on state, and the extra safety is worth the UX impact (like with an online banking portal).
Discussions about this often wind up with a lot of people saying "GET requests aren't supposed to change state!!!", which is true, but just because they're not supposed to doesn't mean there aren't some floating around in large applications, or that there aren't clever ways to abuse seemingly innocuous side effects from otherwise-stateless GET requests (maybe just visiting /posts/1337/?shared_by_user=12345 exposes some tiny detail about your account to user #12345, who can then use that as part of a multi-step attack). Setting the strict flag just closes the door on all of those possibilities in one go.
You want lax for the intuitive behavior on navigation requests from other origins. Because there’s no assumption navigation get requests are safe, strict is available as the assumption-free secure option.