I think the only thing that pulls me out of a story faster than overuse of fancy alternatives to "said" is when the writer has an allergy to identifying characters by pronouns or even their names. "The tall one"/"the blond one"/"the firstborn"/etc. It's like a series of little unnecessary riddles getting in the way of what's going on in the scene. It doesn't help paint a picture of the characters involved and sometimes makes it harder to tell how many characters I'm supposed to be keeping track of. Please, I am begging you, just use their names. In most cases, that'll work best and won't feel repetitive to the reader. Besides, I have a hard enough time remembering characters' names when they appear the right amount in the story!

The main exceptions that come to mind are:

If the PoV character doesn't know names of other characters yet, it's a good opportunity to think about which physical trait would jump out at them most, but this is probably best as a short-term strategy and they should learn names quickly.

If the characters you aren't naming are too minor to bother giving names, such as a group of vampire goons Buffy has to fight, pronouns and one memorable descriptor each should be enough to get her to the end of combat. "Goatee Guy," "Bad Bangs," "Sewer Breath," etc. Sometimes it's funny to go even more basic and identify them as "Goons 1, 2, and 3."

If you're writing about a character who is particularly defined by their profession or a certain descriptor, using that one repeatedly to identify them can be very effective. For example, in the Witcher books, the omniscient narrator uses "the Witcher" more often than "Geralt," which works very well in a setting where the general public is highly suspicious of Witchers and questions their humanity, and sometimes Geralt himself isn't so sure about his capacity for human emotion.

The main point remains, though, that using a wide array of descriptors in all the places where a pronoun or name will suffice can be very ineffective and distracting.

Only 11 days left! I'm in trouble!