Generic word for hyphen, dash, minus sign, etc.?

Unicode calls these code points ones that have the “Dash” (well, or “Dash=Yes”) character property:

U+002D ‭ -  HYPHEN-MINUS
U+058A ‭ ֊  ARMENIAN HYPHEN
U+05BE ‭ ־  HEBREW PUNCTUATION MAQAF
U+1400 ‭ ᐀  CANADIAN SYLLABICS HYPHEN
U+1806 ‭ ᠆  MONGOLIAN TODO SOFT HYPHEN
U+2010 ‭ ‐  HYPHEN
U+2011 ‭ ‑  NON-BREAKING HYPHEN
U+2012 ‭ ‒  FIGURE DASH
U+2013 ‭ –  EN DASH
U+2014 ‭ —  EM DASH
U+2015 ‭ ―  HORIZONTAL BAR
U+2053 ‭ ⁓  SWUNG DASH
U+207B ‭ ⁻  SUPERSCRIPT MINUS
U+208B ‭ ₋  SUBSCRIPT MINUS
U+2212 ‭ −  MINUS SIGN
U+2E17 ‭ ⸗  DOUBLE OBLIQUE HYPHEN
U+2E1A ‭ ⸚  HYPHEN WITH DIAERESIS
U+2E3A ‭ ⸺  TWO-EM DASH
U+2E3B ‭ ⸻  THREE-EM DASH
U+301C ‭ 〜 WAVE DASH
U+3030 ‭ 〰 WAVY DASH
U+30A0 ‭ ゠ KATAKANA-HIRAGANA DOUBLE HYPHEN
U+FE31 ‭ ︱ PRESENTATION FORM FOR VERTICAL EM DASH
U+FE32 ‭ ︲  PRESENTATION FORM FOR VERTICAL EN DASH
U+FE58 ‭ ﹘  SMALL EM DASH
U+FE63 ‭ ﹣ SMALL HYPHEN-MINUS
U+FF0D ‭ － FULLWIDTH HYPHEN-MINUS

There used to be a “Hyphen” property, but now that there are various sorts of word-break properties, the “Hyphen” property has been sent off to retirement.

In typography, there are three common units - hyphen, en-dash and em-dash in ascending order of length. There are divergent rules as to which is to be used for various purposes. One such discussion is found here.

In general, the hyphen is used for splitting words at sentence end and in compound words. The en-dash is used for ranges of numbers and the minus sign, and the em-dash is used to indicate a parenthetical or break in thought.

There doesn't seem to be a single word describing the entire group. If you used any of the terms, I think you would be understood.

dash family

family of dashes

various dash symbols

the various dashes

Some writers have used horizontal line character as a hypernym for the class of character elements with the description of "horizontal line" of various lengths. In addition to the more common hyphen and minus-sign, this group may include the underscore, the overbar and the overstrike elements as well as probably the line segments for forming table borders.

All possible words and phrases seem to have been taken leaving nothing for the hypernym. "Horizontal bar" could have been a convenient option if only it were not taken for U+2015 — unfair!.

[emphasis mine]
typophile wiki:

Indices : Terminology/Characters : En Dash
A horizontal line character one en in width—-half of an em space.

Microsoft Support:

You can also use horizontal lines of different sizes and vertical positions to supplement the dash and underline characters found on the keyboard. Other line styles include the Times Roman characters 150 (em dash) and 151 (en dash) and the Symbol characters 45 (similar to a keyboard dash, but longer) and 190. The em and en dashes are also available in most standard fonts. The Symbol character 190 is the longest available horizontal line character.