Taft had a short term, but an incredibly storied and wild career as a politician outside of (and in cahoots with) the Oval Office.
Speaking to my own field of research, Taft is the reason why the United States consolidated hegemony over the Philippines after they won it from the Spanish with the Treaty of Paris in 1898 (along with Puerto Rico, Guam, and Cuba). Taft led the transition from formal military occupation of the Philippines after the Spanish-American War into a "Civil Government"--ironically named because the establishment of a civil government pretty much was put in place to allow the United States and the world to conveniently forget about the fact that they were still at war with Filipino revolutionaries until well into the 1910s. This irony was probably most clear when Taft was appointed as Secretary of War in 1904 (after an "official end" to the war) which allowed him to stay in the Philippines to manage the new colony.
Even during his short presidency, the Philippine obsession remained--and, if anything, the Oval Office's interior decorating looked a lot better during the Taft Administration. He had a more than healthy obsession with Filipino woodwork and furniture. (But I digress.)
In terms of "domestic" policy (in quotes because I tend to look at Taft as a foreign affairs and imperial president), he was a big supporter of open immigration. He vetoed a law (with the support of the white supremacist--at the time--workers' unions) that restricted unskilled labour through literacy testing. So you can see how these discussions inform our current debates of open immigration, cultural barriers, the "points systems," (especially post-1965) and language.
But even these "domestic" concessions were ultimately informed by foreign affairs. As Governor-General of the Philippines, Taft advocated for the non-implementation of the Chinese Exclusion Act in the Philippines, so that the United States occupying administration would have enough labour resources to build railroads, highways, and other infrastructure to consolidate their rule--and they didn't trust native Filipinos with the work out of fear that they were lazy and unqualified.
Tl;dr: Taft wasn't the most storied president, but as a politician overall, you'd be hard pressed to find someone else besides Truman and Bush (both of them) whose hands weren't dipped into foreign policy as much as his were.
Sources:
Philippine Commission Reports, 1899-1904
David Brody, Visualizing American Empire
Vicente Rafael, White Love and Other Events in Filipino History
Paul Kramer, The Blood of Government
Kornel Chang, Pacific Connections (especially for migration and unions' white supremacy)
The breakup of Standard Oil happened under Taft's Presidency. Indeed, Taft broke up more trusts than Tesdy Roosevelt himself.
Taft was an amazing politician, but his greatest legacy is as the only President to also serve as Chief Justice of the Supreme Court. He wrote deciding insular cases, such as Balzac v. Puerto Rico: https://scholar.google.com.pr/scholar_case?case=8956361016270671048&q=balzac&hl=en&as_sdt=2003. The case established that Puerto Rico was non-integrated territory, and that constitution does not "follow the flag." As non-integrated territory, PR and the other U.S. island colonies belong to, but are not a part of, the United States. They have no state rates and are not subject to the equal spending clause of the constitution. Only those rights determined by the federal government as "fundamental," (i.e. individual rights such as freedom of speech and religion), are protected. The colonies do not have "procedural" rights guaranteed by the constitution, such as trial by jury, or states rights, which means they are unrepresented in Congress and cannot vote for president. For the four million citizens of the U.S. Island Colonies, Taft's legacy as Chief Justice of the Supreme Court has more impact that his short presidency.