How to describe a cloak touching the ground behind you as you walk?

It is odd to say "his cloak trailed the ground", while "trail" can be a transitive verb, it means to track when used in this way. You might want to say "his cloak trailed along the ground". You could also say "his cloak swept the ground behind him". That has a somewhat more literary tone. Or "his cloak brushed the ground" if you wanted to indicate that the cloak was not constantly in contact with the ground, but made occasional contact as he walked.

You might use the word or allude to 'train' if you feel it is warranted, which is what a wedding garment that follows a bride in a similar way is called. https://www.brides.com/story/wedding-dress-train-etiquette

drag:

3 : to move or cause to move along on the ground You're dragging your scarf. Your scarf is dragging

https://www.merriam-webster.com/dictionary/drag

Remember to keep track of what the subject and object of a verb can be. "Trail" and "drag" both have the cloak as the direct object. The ground would be an indirect object: "The cloak dragged on the ground". There are verbs for which "the ground" can be a direct object, such as "scrape".

It’s normal for some styles of cloak to touch the ground. Here are some examples: https://www.yourdressmaker.com/capes-and-cloaks-2#/pageSize=12&orderBy=0

Most readers have a “reasonable” knowledge of clothing. They know that shorts are shorter than pants. They know that a cloak covers more than a cape. However, you can’t count on them knowing the exact length of a specific style.

This means that you can choose words that give your reader additional information.

If your intent is simply to describe the cloak, you can simply refer to it as floor length or full length: He wore a floor length cloak, perfectly fitted. It trailed lightly behind him as he walked.

Your choice of words for how the cloak touches the ground is related to how the cloak is supposed to touch the ground, and this depends on how the garment has been fitted to the wearer.

Generally speaking, a well-fitted garment is described in positive terms, e.g. they were fitted out identically in ceremonial garb, but the richer men with better tailors were instantly obvious. Their cloaks brushed delicately against the flagstones as they moved in dignity up the aisle. The poorer men clutched and dragged as best they could.

Use brushed if it occasionally touches and brushes for a longer cloak. Use dragged/dragging or catched if the touching significantly impedes movement.

Sweep

The cloak was long enough to sweep the ground behind him

Verb scuff (or more likely scuffed) is the word I'd use. It means light brushing and has the advantage of being onomatopoeic.

His radiant form caused the ground to disappear beneath him as he walked, so that everyone who gazed upon him began to glimpse that he was emerging from another dimension, and so that his magical cloak seemed to flow gently as if in a breeze, even though his cloak was long enough to otherwise have touched the mysteriously disappearing earth.

Cloaks probably shouldn't touch the ground.

Okay, I'm going to give a frame challenge here: in any historical (or pseudo-historical fantasy) setting, cloaks probably shouldn't be long enough to touch the ground. The ground is dirty, and keeping it clean of dust and dirt is difficult, requiring the active labor of servants, possibly on a daily basis. Remember, there were no vacuum cleaners back then, so to keep a room clean, they'll need to sweep and dust it all by hand.

Additionally, once such a cloak became dirty, cleaning it would require even more manual labor. Remember, washing machines didn't exist yet either, so cleaning clothes required very physically-intensive manual labor (wet cloth is heavy).

I wonder nobody has suggested kiss yet.

to strike lightly; brush against

[American Heritage Dictionary]

His cloak was long enough to kiss the ground behind him.