I started to work with Paletton.com. I need to get color scheme to Adobe Illustrator. I see .aso among output (export) formats in Paletton and I understand that I can load this .aso in Photoshop, then export those swatches in .ase (exchange) format and finally open this .ase in Illustrator. This method works but I am wondering if there is a better and quicker workflow to get colors from Paletton to Illustrator. Thank you.
I can't help you directly with paletton, but I made a tool for creating and exporting color palettes to ASE format, amongst other stuff.. (sidesketch.com). It's a little rough around the edges still, but it might help you out.
For example, here's some of the material UI colours - https://sidesketch.com/palette/73 - hit 'adobe swatch' and you can import the created ASE file directly into AI.