*The redly highlighted word caught her eye.

The problem you have is that the action of highlighting was not done "redly" and an adverb is not appropriate. Next, redly does not mean "in red."

"His face coloured redly" is not the same as "His face coloured in red."

"The redly highlighted word caught her eye." is not the same as "The word highlighted in red caught her eye."

You wish to describe the state of the highlighting as "red". States are described by adjectives.

You need to look at the differences between adjuncts and adverbs and adjectives.

Redly, bluely, blackly, etc. all exist but are required to be used in the correct context.

*The redly highlighted word caught her eye.

The problem you have is that the action of highlighting was not done "redly" and an adverb referring to a colour is not appropriate. Next, redly does not mean "in red."

"His face coloured redly" is not the same as "His face coloured in red."

"The redly highlighted word caught her eye." is not the same as "The word highlighted in red caught her eye."

You wish to describe the state of the highlighting as "red". States are described by adjectives.

You need to look at the differences between adjuncts and adverbs and adjectives.

Redly, bluely, blackly, etc. all exist but are required to be used in the correct context.