How many US presidents were of Welsh extraction?

The Welsh have shaped American history more than most people realize. Seventeen signers of the Declaration of Independence were of Welsh extraction, as were ten US Presidents. Thomas Jefferson actually spoke Welsh.
http://www.britam.org/now2/1550Now.html

America's past presidents and vice presidents of Welsh descent include Abraham Lincoln, James Monroe, Richard Nixon, Hubert Humphrey, Calvin Coolidge and Andrew Jackson. Thomas Jefferson, the great American Statesman spoke Welsh, his family came from Snowdonia.
[thewelshwizard.com/LIST/WALES.HTM, no longer online]

The book reveals that Wales even has links to the White House. Mr Breverton said: "Five of the first six American presidents were of Welsh extraction. In the history of America we are absolutely amazing. The greatest architect Frank Lloyd Wright, the greatest film director D.W. Griffith - both Welsh people."
http://www.walesbooks.com/reviews5.php

Five of the first six Presidents of the USA were of Welsh descent, and the ten Presidents to date with Welsh connections include, John Adams, John Quincy Adams, Thomas Jefferson, James Morrison Jnr, James Monroe, William Harrison, Abraham Lincoln, Benjamin Harrison, James A Garfield and Calvin Coolidge.
http://www.abergavennychronicle.com/article.cfm?id=102901

This site seems to contradict the others somewhat and lists only these Presidents with Welsh blood:

(13) Fillmore and Pierce (both almost entirely English with just a smidgeon of Welsh);

(17) Grant (Scots-Northern Irish, Irish?, Walloon, French, Welsh?, the rest English);

(20) Arthur (English, Irish, Scottish and Welsh in more or less equal quantities);

(23) Theodore Roosevelt (mostly Dutch of course, but very nearly as much Scottish; moreover a Yates ancestor was English but married into a Dutch family and the descendants for a generation or two are documented as having Dutch forenames although the surname remained Yates; Roosevelt was also a little bit French, Irish and Welsh);

(30) Truman (certainly Scottish plus possibly Welsh and English on his father's side; a surprisingly strong German showing on the mother's side);

(34) Nixon (strong Irish descent, plus a Welsh and English strain);

[burkes-peerage.net/sites/america/sitepages/page73-3.asp, no longer online]

Barack Obama has Welsh ancestry as well. At the beginning of the 19th century, his great-great-great-great-great-great-grandparents Henry and Margaret Perry emigrated from Anglesey to Ohio.

https://www.walesonline.co.uk/news/wales-news/wales-link-presidential-candidates-past-2162435?_ga=2.252458889.1893957163.1607723382-2066391646.1607723382