I suspect it's contrary to your objective of having attractive tile on which to walk, but there are a number of grip-enhancing paints on the market. Many are described as driveway paint with grip or driveway paint with grit.
Other links suggest adding job-specific grit to paint and from there one could extrapolate that the same grit could be added to a clear surface treatment.
Grit embedded tape is also on the market, far less attractive than a painted surface (opinion) and subject to unsightly wear.
An additional thought popped into my alleged mind. There is a product called Never-Wet, which is a hydrophobic coating. It's marketed under the Rustoleum™ brand and available at many big-box stores and Amazon. I have a package (somewhere) but have never used it. I recall the package instructions indicating that there's a slight cloudy effect to the application on some surfaces, primarily fabrics. I suspect that would not be a problem on the tile.
As water is creating the slippery effect, perhaps Never-Wet would remove the water and therefore the slippery.
A final resort would be to hire a portable sandblaster vendor or device and remove the slippery glaze of the tile. The coloration would likely remain but become subdued. Perhaps even a floor sander or similar device would enable suitable roughness.
Photo from Amazon link.