Why does only the cis-isomer of potassium dioxalatodiaquochromate(III) form?
I'm not an inorganic chemist, but to my understanding, both cis- and trans-dioxalatodiaquochromate(III) ions exist (Note that some also called it as Diaquabis(Oxalato)Chromate (III)). According to what I found online is that solid state reaction gives cis-form while aqueous reaction predominantly forms trans-isomer (it is mentioned in one of your attachments). However, it's still up to debate.

Hamm in 1952 had shown that trans—cis Isomerization using UV-vis spectroscopy ($trans \rightarrow cis$; Ref.1). According to Hamm, all previous workers have prepared trans-isomer because its lack of solubility. Yet, the existence of cis- and trans-isomers has been first recognized by Werner and has presented the preparation methods of two isomers individually (Ref.2), thus it is not true that the your concept of only the cis-stereoisomer forms.

Werner had mentioned that aqueous solution of trans-isomer is stable only in the cold temperatures. That may be the reason why only cis-isomer forms in solid state preparations because the preparation needs heating at high temperature.

Using the method given by Werner, trans-dioxalatodiaquochromate(III) isomer has been prepared and its crystal structure has been studied (Ref.3 &amp; 4). 

Later studies have showed this trans-isomer converted to cis-isomer by long standing in aqueous solutions (Ref.5). Based on their results, the authors have concluded that these color changes (dark red trans-isomer to blue cis-isomer) are due to trans–cis isomerization, uncomplicated by olation phenomena and that the transformation to the cis configuration proceeds to practical completion. They also stated that:


  Kinetically, the reaction (trans–cis isomerization) obeys a first-order law, and the dependence of the observed velocity constant upon temperature is found to be adequately described by the Arrhenius equation, where $A = 3 \times 10^9$ and $E = \pu{−17.9 kcal/mol}$. 


Finally, in recent studies have been done on computational analysis of trans- and cis-Isomers of Potassium dioxalatodiaquochromate(III). The studies revealed that  cis-Isomer is slightly stable than trans-Isomer (Ref.6):


  The trans- and cis-isomers of potassium diaquabis(oxalato)chromate (III) were studied computationally and experimentally. The structures of trans- and cis-configurations of $\ce{[Cr(H2O)2(C2O4)2]-}$ were optimized by DFT methodology with various functionals namely: B3LYP, CAM-B3LYP, TPSS, PBE, M06-L and ωB97X-D along with the more sophisticated MP2 method. The calculations show that the most stable forms for both isomers are in quartet states. The results from all DFT methods reveal that the cis-isomer is literally more stable than the trans-isomer with the lower average relative energy of $\pu{2.1 kcal/mol}$. These are consistent with the results from MP2 calculation and experimental observation. The absorption wavelengths for the excited states of trans- and cis-structures were calculated by the time-dependent density functional theory (TDDFT) method. For the experiments, the trans- and cis-isomers of potassium diaquabis(oxalato)chromate (III) were synthesized and characterized by UV-Vis spectrophotometry. Both isomers have two maximum absorption wavelengths at $415$ and $\pu{560 nm}$.


References:


Randall E. Hamm, “Complex Ions of Chromium. II. trans—cis Isomerization of Potassium Dioxalatodiaquochromate(III),” J. Am. Chem. Soc. 1953, 75(3), 609-611 (https://doi.org/10.1021/ja01099a026).
A. Werner, W. J. Bowis, A. Hoblik, H. Schwarz, H. Surber, “Über Metallverbindungen mit komplex gebundener Oxalsäure. Zweite Mitteilung: Über Dioxaloverbindungen),” Justus Liebigs Annalen der Chemie 1914, 406(3), 261-331 (https://doi.org/10.1021/ja01099a026).
J. N. van Niekerk, F. R. L. Schoening, “Structure of Trans-Potassium Dioxalato-Diaquo-Chromiate,” Nature 1950, 166, 108 (https://doi.org/10.1038/166108a0).
J. N. van Niekerk, F. R. L. Schoening, “The crystal structure of trans potassium dioxalatodiaquochromiate, $\ce{K[Cr(C2O4)2(H2O)2].3H2O}$,” Acta Cryst. 1951, 4(1), 35-41 (https://doi.org/10.1107/S0365110X51000064).
G. E. Cunningham, R. W. Burley, M. T. Friend, “Potassium Dioxalato Diaquo Chromium (III) Complexes: Trans–Cis Isomerization,” Nature 1952, 169, 1103 (https://doi.org/10.1038/1691103a0).
Songtham Ruangchaithaweesuk, Juthathip Chorkate, Thana Maihom, Potjaman Poolmee, Piti Treesukol, Tipawan Rungsawang, Phornphimon Maitarad, Bundet Boekfa, "Combined Computational and Experimental Studies of Trans- and Cis-Isomers of Potassium Diaquabis(Oxalato)Chromate (III)," Key Engineering Materials 2017, 757, 103-107 (https://doi.org/10.4028/www.scientific.net/KEM.757.103).