The non-migrating chicken is different from the migrating goose; force-feeding will not result in a liver with a significant higher fat content. The chicken liver plays a role in producing fat but not in storing it in itself.
The adipose fat in chicken is mainly in the subcutaneous (under the skin), abdominal (stomach) and clavicular (shoulders) region[1] (study looked at ages 4 and 14 days only). See also another study[3] which is bit broader.
Alshamy et al. [2] found no adverse effects to the livers of chicken under a high energy diet. They compared two different chicken lines, a dual-use line (Lohmann Dual) and a broiler (Ross 308). The Lohmann Dual had 9% more lipids (fat) in the liver than the broiler.
Average fat content in chicken liver (the Korean study I found says "Ross breed" which are broilers but there are many Ross breeds) is about 2.9% for that line[5]. As this is a Korean study it might be interesting to know that the fat content as listed in the USDA is 4.8gr per 100gr (https://fdc.nal.usda.gov/fdc-app.html#/food-details/171060/nutrients).
Geese on the other side need reserve for migration. That reserve is fat and it is mainly stored in the liver[4].
Fat content of Foi Gras (liver of force-fed geese) according to the USDA is about
44gr per 100gr (https://fdc.nal.usda.gov/fdc-app.html#/food-details/171100/nutrients). The product listed in the USDA is canned smoked Foi Gras*. Another, french, source (https://www.lanutrition.fr/bien-dans-son-assiette/aliments/viandes/le-foie-gras-et-votre-sante) has the fat content of raw goose liver ("Foi Gras d'Oie" in French) at ~55gr per 100gr if force-fed.
There seems to be a small movement to use the naturally fattened liver by slaughtering them at the times when they prepare for migration. I can only give the source I found in Wikipedia that a Spanish company won a French price (https://web.archive.org/web/20071128130319/http://www.regiondigital.com/modulos/mod_periodico/pub/mostrar_noticia.php?id=47071) for their Foi Gras produced without force-feeding. An animal friendly (besides the slaughtering) Tournedo Rossini? Mmmh, I wish I could afford that!
If you are not familiar with the recipe for Tournedos Rossini: it is basically a thick slice of roasted Brioche topped by a nice tournedo topped by a thick slice of Foi Gras topped by a thick slice of black truffle (Perigord truffle, Tuber melanosporum) topped by a generous ladleful of Madeira sauce.
[1] Shiping Bai et al. "Broiler chicken adipose tissue dynamics during the first two weeks post-hatch", Comp. Biochem. Physiol. A Mol. Integr. Physiol. 2015 Nov;189:115-23, DOI: 10.1016/j.cbpa.2015.08.002 , abstract at https://pubmed.ncbi.nlm.nih.gov/2626385
[2] Z. Alshamy et al. "Structure and age-dependent growth of the chicken liver together with liver fat quantification: A comparison between a dual-purpose and a broiler chicken line" in PLoS One 2019 Dec 27;14(12):e0226903.. https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0226903
[3] A. M. Fouad et al., "Nutritional Factors Affecting Abdominal Fat Deposition in Poultry: A Review" in Asian-Australas. J. Anim. Sci. 2014 Jul; 27(7): 1057–1068. at https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4093572/
[4] Guosong Wang et al., "Transcriptomic analysis between Normal and high-intake feeding geese provides insight into adipose deposition and susceptibility to fatty liver in migratory birds" in BMC Genomics volume 20, Article number: 372 (2019). at https://link.springer.com/article/10.1186/s12864-019-5765-3
[5] Pil Nam Seong et al., "Characterization of Chicken By-products by Mean of Proximate and Nutritional Compositions", Korean J. Food Sci. Anim. Resour. 2015; 35(2): 179–188. at https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4682518/
* Smoked? Really?