It’s often claimed that the push to replace the Articles of Confederation with a new Federal government was due to the perceived need for a stronger central government, which the new Constitution certainly provided. But at the same time the Federalists were apparently in reaction against populism, to the point that the new Federal government was to be only very indirectly answerable to the people. These seem to me like two separate and only distantly related issues, and afaik the state governments were neither more nor less populist before or after the switchover. So how and why did the two issues become conflated?
To answer the easiest part of your question first, this statement is correct. The Constitution of the United States (COTUS) had little affect on the structure or function of state governments, other than restricting their powers in certain limited domains. Some states (for example, Pennsylvania) were more populist than others (for example, South Carolina) in 1787, and they remained that way in 1789.
The COTUS created a more powerful federal government, due to perceived weaknesses in the Congress under the Articles of Confederation in servicing its debt and conducting foreign policy. The new government had to lean toward the less populist end of the spectrum; else persons fearful of change would not have supported it. Even so the House of Representatives, the equivalent of the all-powerful British House of Commons, was directly answerable to the people. and the Senate and the President were answerable at one step removed via the state legislatures and the electoral college, respectively.
I assume even back then the southern states feared anti-slavery sentiment and wanted to be sure the government was not susceptible to waves of populist impulses.