He definitely wasn’t a democratic socialist. He was an establishment Democrat. He grew up rich and had a very distinguished pedigree. His life is a study in privilege:

Franklin Delano Roosevelt was born on January 30, 1882, in Hyde Park, New York, to businessman James Roosevelt I and his second wife, Sara Ann Delano. His parents, who were sixth cousins,[3] came from wealthy, established New York families—the Roosevelts, the Aspinwalls and the Delanos, respectively. Roosevelt’s father, James, graduated from Harvard Law School but chose not to practice law after receiving an inheritance from his grandfather.

As a child, Roosevelt learned to ride, shoot, sail, and play polo, tennis, and golf.[8][9] Frequent trips to Europe—beginning at age two and from age seven to fifteen—helped Roosevelt become conversant in German and French. Except for attending public school in Germany at age nine,[10] Roosevelt was homeschooled by tutors until age 14. He then attended Groton School, an Episcopal boarding school in Groton, Massachusetts.

Like most of his Groton classmates, Roosevelt went to Harvard College.[12] He was a member of the Alpha Delta Phi fraternity[15] and the Fly Club,[16] and served as a school cheerleader.

Roosevelt entered Columbia Law School in 1904 but dropped out in 1907 after passing the New York Bar Examination.[24][b] In 1908, he took a job with the prestigious law firm of Carter Ledyard & Milburn, working in the firm’s admiralty law division.

In 1903, Franklin proposed to Eleanor. Following resistance from his mother, Franklin and Eleanor Roosevelt were married on March 17, 1905.[12][28] Eleanor’s father, Elliott, was deceased; Theodore, who was then president, gave away the bride.[29] The young couple moved into Springwood. Franklin and Sara Roosevelt also provided a townhouse for the newlyweds in New York City, and Sara had a house built for herself alongside that townhouse. Eleanor never felt at home in the houses at Hyde Park or New York; however, she loved the family’s vacation home on Campobello Island, which Sara also gave the couple.

https://en.wikipedia.org/wiki/Franklin_D._Roosevelt

Is there any specific political ideology that talks about workers seizing means of production via this manner (the state forcing businesses to become cooperatives)?

You mean kids? For real i dont think theres any serious political movement that is so naive

Additionally:

The Twenty-second Amendment to the United States Constitution, which established presidential term limits, was ratified on February 27, 1951.

Prior to the ratification of the Twenty-second Amendment, there were no formal term limits for the U.S. presidency. The tradition of a two-term limit was established by George Washington, but this was not legally binding.

FDR died in 1945. The entire thing is false propaganda rage bait.

ELI5 please?