How to catalog a Haggadah which is entirely in romanized Hebrew and consists of excerpts that,  evidently,
have been designated to be sung during the seder?

Descriptive cataloging

The 130 will be "Haggadah. Selections"

As for the later part of the query: when a liturgical work doesn't come right out and say that it's a non-traditional rite (Ari, or whatever), we usualy default, in descriptive, to Ashkenazi.  If someone comes along later and points out to us that, though it doesn't say so, it really IS some other version, we'll change it.

Subject analysis

Presuming that the text solely contains songs from the Haggadah, it should be assigned 130 Haggadah. Selections.
Based on the u.t., and presuming that the work doesn't include translations or musical score, we recommend the following subjects:

     650  0 Seder$xLiturgy$vTexts.
     650  0 Judaism$xLiturgy$vTexts.
     650  0 Passover music$vTexts.

and class:
     BM674.6

If the book contains song texts that are NOT the normal  songs forming part of the Haggadah liturgy (Had gadya, etc), but just
some nice songs having something or other to do with Passover, all the above comments for cataloging the thing are moot.

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Whether the item is a Haggadah text without commentary, text with commentary, or commentary alone (or even commentary with all or some text) is reflected both in the descriptive and subject cataloging elements, as applied on LC's Hebraica Team.

The appearance of the text is reflected, as was suggested, by the presence of a uniform title either as the main entry, or as an added entry, depending upon the presentation of the chief source. (I will defer to the descriptive cataloging experts to elaborate.)

With regard to the subject heading assignment, we apply the guidelines of the Subject Cataloging Manual, H1435, Commentaries.  If the work is solely or primarily commentary, the first subject heading assigned is the uniform title for the work, Haggadah.  Additional subjects are generally assigned to reflect those assigned to the original work, and vary slightly depending on whether the text is included in the work in-hand or not.

TEXT ALONE
Haggadot--Texts.
Seder--Liturgy--Texts.
Judaism--Liturgy--Texts.

TEXT WITH COMMENTARY
Haggadot--Texts.
Seder--Liturgy--Texts.
Judaism--Liturgy--Texts.
Haggadah.

COMMENTARY WITHOUT TEXT
Haggadah.
Seder--Liturgy.
Judaism--Liturgy.
 
COMMENTARY WITH TEXT
Haggadah.
Haggadot--Texts.
Seder--Liturgy--Texts.
Judaism--Liturgy--Texts.

Armed with such information, and depending on the capabilities of the system (as well as the consistency of the cataloging) the searcher should be able to combine (or narrow) searches of descriptive and/or subject access points to find what s/he wants.

Lenore Bell