The variants -gena and -genus
This ending has two forms: -gena (inflected as a first-declension masculine/common gender noun, potentially used adjectivally) and -genus, -gena, -genum (inflected like a first/second declension adjective).
I believe second declension variants in -genus, -genum etc. are generally rare in ancient times, and become more frequent in later texts. For example, there are no hits for indigenu or indigeno in the PHI Latin corpus, but this variant of indigena can eventually be found in later sources (the Lewis and Short entry indicates that indigenum sermonem can be found in at least some versions of Apuleius's Metamorphoses, although I've also seen editions that give it as "indigenam sermonem"), with apparently the same meaning as indigena.
The primary meaning seems to be "born"
I think the usual meaning of -gena and -genus is "born".
The ending I would expect for words meaning "X-bearing" is -fer or -ger.
Aside from your example of Aquinas's "deigena deitas", which I'm not sure how to interpret, there are the following possible cases of -genus/-gena meaning "bearing":
florigenus, per L&S "producing blossoms, blossoming"
puerigenus per L&S "that begets boys"
monstrigenus/monstrigena per L&S "monster-bearing" (pointed out in a comment by cmw)
morbigenus per DMLBS "disease-bearing, that causes illness" (via Logeion)
nubigenus "cloud-bearing" per Gaffiot 2016 (via Logeion)
ignigenus per L&S "producing fire" (of a donkey whose pack was on fire)
omnigenus per L&S "all-begetting, all-producing (postclass.)"
I think cmw's comment attributing these kinds of examples to "post-classical misinterpretation" of the meaning of the suffix is the correct explanation.
In the course of Googling this suffix, I actually came across an assertion by Josef Niederle ("Proposals to add examples of correct usage of Latin compounds to Article 23", TAXON 65 (2) • April 2016: 415), that the variation in form between common-gender nouns in -gena and 1st/2nd-declension adjectives in -genus, -gena, -genum has a direct correspondence (in "correct usage") to the difference in meaning between "-born" and "-bearing". However, given the existence of counterexamples of words in -genus used with the sense "-born" (which Niederle dismisses as erroneous usages), I'm inclined to disagree: I think that there is only an indirect correlation, in that both the use of the form -genus and the sense "-bearing" both appear to become more common post-Classically.
Word formation: the linking vowel -i-
Since words ending in -gena/-genus are compounds, they usually have the format "stem" + "linking vowel -i-" + "ending". For example, montigena "mountain-born" from mons, montis and terrigena "earth-born" from terra, terrae show that -i- is not restricted to occurring in words formed from nouns with genitives in -ī. Also, the interfix or linking vowel -i- that we find in compounds is a short vowel, while the second-declension genitive ending -ī is a long vowel.
Therefore, my conclusion would be that "librigena" is validly formed from liber and -gena, but would be more likely to mean "book-born" than "book-bearing".