Yes, the actual time interval measurements recorded from atomic clocks that demonstrate the reality of time dilation have been published in scientific literature. Numerous experiments have been conducted to measure and verify the effects of time dilation predicted by the theory of relativity.
One prominent example is the Global Positioning System (GPS), which relies on precise timing measurements. The satellites in the GPS system have atomic clocks on board, and these clocks are used to provide accurate timing information for navigation purposes. The clocks on the satellites experience both the effects of special relativity (due to their high speeds) and general relativity (due to the weaker gravitational field in space).
To account for the predicted time dilation effects, the clocks on the satellites are adjusted or corrected based on the known relativistic factors. The corrections are necessary to maintain accurate synchronization with clocks on the Earth's surface.
The data from these measurements and adjustments have been published in scientific papers and technical reports. For example, the U.S. Naval Observatory, which operates the Master Clock for the GPS system, has published technical documents detailing the relativistic effects and the corrections applied to the satellite clocks.
In addition to GPS, other experiments have been conducted to directly measure time dilation due to relative motion and gravitational fields. These experiments involve comparing highly accurate atomic clocks that are placed at different locations and subjected to different gravitational fields or relative velocities. The differences in the clock rates provide direct evidence of time dilation.
While I cannot provide specific numbers or references to the most recent publicationsof 2023, there is a wealth of scientific literature available that presents and discusses the experimental measurements confirming time dilation. These publications are found in journals, conference proceedings, and technical reports in the field of physics.