The date of American Thanksgiving was first set by Abraham Lincoln in November 1863 in thanks for the Union victory at Gettysburg in the summer of that summer.
Not quite. We're dealing with the evolution of a tradition of locally-proclaimed spontaneous days of thanksgiving into a national holiday with a date set by law.
There has been a federally proclaimed/legislated Thanksgiving day every year since Lincoln's 1863 proclamation, but the holiday was already widely celebrated as an annual thing before that (at the initiative of state/local governments with dates close to the modern one), and for many years afterward, while it was proclaimed federally every year, the President still had to take action to proclaim it, and was not actually obligated to do so...
FDR tweaked the date to the current third Thursday of November and that's when it was really generalized as the Pilgrim's harvest festival we see it for now.
...FDR tried moving it from the last Thursday to the second-last. November of 1939 had five Thursdays (with the fifth being in the 30th), and because at that time it was still seen as gauche for retailers to start preparing for Christmas before Thanksgiving, there was allegedly some lobbying to have Thanksgiving occur earlier. Because it was still entirely his initiative to do so, FDR proclaimed Thanksgiving for the 4th Thursday that year, and the 3rd the next two years, which caused a fair amount of backlash. Congress then legislated a date for Thanksgiving, and it's officially been the 4th Thursday ever since (which was a compromise between the traditional last Thursday and FDR's second-last).
I think the association of Thanksgiving specifically with the pilgrims has as much to do with Lincoln's proclamation as anything: small-t thanksgiving services had been held in several colonies in Virginia before the pilgrims ever landed, and the communities associated with those colonies have made their own claims to having had the "First Thanksgiving" (though I think only Jamestown has actual continuity with its original colony), but Lincoln's proclamation made Thanksgiving unpopular in the South (because Lincoln) until football made it popular again in the 20th century. Thanksgiving being unpopular in the South impeded the ability of the Virginia communities that had celebrated early thanksgivings to press their claims. Since the Plymouth colony was the oldest in the North, its story was the one that got told.
But my real point regarding the pilgrims was that you can't trace Thanksgiving back to a specific European holiday: The Puritans didn't have set holidays, so even if you trace Thanksgiving specifically back to their small-t thanksgiving after their first harvest,
they never made it an annual thing because they didn't
do annual things, nor, for the same reason, can you trace it past that. And if you bring in the Virginian claims, the frequent proclamation early on of one-off days of thanksgiving, and the presence of other occasions for thanksgiving (such as Evacuation Day) that helped to establish a late November date before Lincoln's proclamation, the connection to any specific European holiday becomes even harder to make.