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Article I, Section 8 states that "The Congress shall have Power... To establish Post Offices and post Roads."
Note that this is phrased as a power of Congress, not an entitlement for the people. The exact form that the national postal system has taken over the years has changed with time according the changes in federal laws.
See here for more information: https://about.usps.com/who-we-are/postal-history/
The federal constitution is silent on the topic of public education, and the federal government played little to no role in the general public education of your average American student until the 20th century. Even with the creation of federal education programs in the 20th century, they have mostly been supporting the role of the states rather than as the primary authority in providing for education. There has also never been a federal requirement that states create a public education system.
However, under the 14th Amendment, IF a state does create a public education system, then that education system must be provided equally to all, without discrimination. The federal government has at times involved itself in state education systems in order to enforce 14th Amendment rights.