What is the pKa of iodous acid?
According to Schmitz [1], $\mathrm{p}K_\mathrm{a}(\ce{HIO2})\approx 6$ at $\pu{25 °C}$ (numerical references for the bibliographical entries have been updated):

Stanisavljev [2] has proposed a correlation between thermodynamic values of oxo-halogen ions and has obtained $ΔG_\mathrm{f}^\circ (\ce{IO2-}) = \pu{−51.8 kJ mol−1}$. He has also estimated the dissociation constant of $\ce{IO2H}$, $\mathrm{p}K_\mathrm{a}(\ce{IO2H}) = 4$, and obtained $ΔG_\mathrm{f}^\circ (\ce{IO2-}) = \pu{ −75 kJ mol−1}$. However, this value introduced in the above equation leads to $K_\mathrm{C}^\circ = \pu{2.8e12}$ and an impossibly large value of $k_\mathrm{+C}^\circ$. His correlation supports the idea that $k_\mathrm{+C}^\circ$ is very large but overestimates $ΔG_\mathrm{f}^\circ (\ce{IO2-})$ and probably also the dissociation constant of $\ce{IO2H}$. Figure 1 shows known $\mathrm{p}K_\mathrm{a}$ values of oxy-halogen acids, including the value of $\mathrm{p}K_\mathrm{a}(\ce{BrO2H})$ [3] not considered by Stanisavljev, and suggests that $\mathrm{p}K_\mathrm{a}(\ce{IO2H})$ is closer to $6$ than to $4$.

Figure 1. $\mathrm{p}K_\mathrm{a}$ values of oxy-halogen compounds $\ce{XOH}$ (•) and $\ce{XO2H}$ (◦).

References

Schmitz, G. Inorganic Reactions of Iodine(III) in Acidic Solutions and Free Energy of Iodous Acid Formation. International Journal of Chemical Kinetics 2008, 40 (10), 647–652. https://doi.org/10.1002/kin.20344.
Stanisavljev, D. Consideration of the Thermodynamic Stability of Iodine Species in the Bray-Liebhafsky Reaction. Berichte der Bunsengesellschaft für physikalische Chemie 1997, 101 (7), 1036–1039. https://doi.org/10.1002/bbpc.19971010708.
Faria, R. B.; Epstein, I. R.; Kustin, K. Kinetics of Disproportionation and $\mathrm{p}K_\mathrm{a}$ of Bromous Acid. J. Phys. Chem. 1994, 98 (4), 1363–1367. https://doi.org/10.1021/j100055a051.