Okay, so I have NO idea how to put this into the guide, but I figured out how to add, edit, and view tile properties in Tiled, and how to animate tiles.
The map in the screenshots is an edited version of the Lowkey Lux Slime Hutch Spa mod. It's a personal edit that makes the mod compatible with the Bath House Hot Spring mod. Presently it is for personal use only, and I have no plans to release it to the public at this time as I do not have the permission of either mod author to release it publicly.
To Add Tile Properties:
A small note: this works best when "Snap to Grid" is enabled in the "View" menu, since otherwise your objects will not be constrained to the tile grid in tIDE when you return it to tIDE to convert it from .tmx to .tbin.
Add the type of property in the window that comes up. Note, I'm not 100% certain what the other properties there are, but the ones that Stardew uses all appear to be "string" properties. (https://gyazo.com/d9803851efede58ccf42a27abfffe5de)
Click and drag the tiles you want animated into the left panel. By default, the length of the animation will be 100ms; Stardew's animation lengths vary between 250ms and 1000ms. Change the animation length as desired by double-clicking on the number after it. Close or minimize the window once you have finished.
You'll notice that the tile now has a little symbol over the bottom-right corner. (https://gyazo.com/357947fa43c7cde689770b125390b9db) Unlike in tIDE, you only need to apply the animation to a particular tile once--after that, all tiles placed on the map that match the one you placed the animation on will have the animation.
Per comment by @SpringsSong on https://github.com/Pathoschild/canimod.github.io/commit/201f7d02d8f5591c00b4a98b5e6385d2579086c5#commitcomment-20655114 (gyazo images attached instead):