Complete Oxidation of Methanol
Although the direct complete oxidation of methanol (or formaldehyde or formic acid, on that matter) to carbon dioxide ($\ce{CO2}$) using  oxidizing reagents such as $\ce{KMnO4}$  or $\ce{K2Cr2O7}$  is hard to find in literature, electrochemical oxidation of methanol to $\ce{CO2}$ through formaldehyde and formic acid is one of the concepts used in fuel cell research (Ref.1). The extensive use of simple organic compounds such as methanol, formaldehyde, and formic acid as fuels is because they have several advantages, likes of being easy to store and handle, and having possess a high energy density of the order of $\pu{kWh/kg}$. Aside from that, one would also expect they should have the simplest and most straightforward reaction mechanisms of all the possible organic fuels because of their simple structure. Yet, in their review article (Ref.1), Parsons and VanderNoot revealed that the oxidation of methanol to $\ce{CO2}$, involves $\ce{6 e-}$ so the oxidation must occur in several steps with several products or intermediates. The product resulting from complete oxidation of methanol (and other individual organic fuels such as formaldehyde and formic acid) is of course $\ce{CO2}$. The reactions of all these three fuels have been studied on a variety of electrodes, and with a wide spectrum of experimental conditions to optimize the outcome (most of those references are sited in Ref.1). Keep in mind that the studies involving methanol are outweighed those of formaldehyde and formic acid, simply due to the fact that its complete oxidation to $\ce{CO2}$, generates 6 electrons compared to 4 and 2 for formaldehyde and formic acid, respectively. Electrode potentials of these reactions are still debatable, and Koppenol and Rush have collected and calculated some reduction potentials for $\ce{CO2/CO2^{.-}}$ couple and plotted them in a Frost diagram (Ref.2).
We noted above that the electrochemical oxidation of methanol to $\ce{CO2}$ involves $\ce{6 e-}$.  As expected, the oxidation occurs in several steps with several products or intermediates, and, for example, mass spectral measurements has showed that both $\ce{H2CO}$ and $\ce{HCO2H}$ were produced (Ref.3).  Their conclution was listed as:

(a) At room temperature, a stationary decomposition of methanol takes place on a platinum catalyst, with formation of formaldehyde and formic acid;
(b) $\ce{HCO2H}$ reacts with $\ce{CH3OH}$ to form $\ce{HCOOCH3}$ (methyl formate);
(c) $\ce{HCO2H}$ is also produced during electrolysis, and is an intermediate in the oxidation to $\ce{CO2}$;
(d) $\ce{H2CO}$ reacts with $\ce{CH3OH}$ to form $\ce{CH2(OCH3)2}$ (methylal), but, contrary to the results of other authors, $\ce{H2CO}$ is not an intermediate of electrolysis.

Accordingly, you’d see even under electrochemical conditions, this conversion is not straightforward. Ref.1 also proposed a step-wise mechanism to explain all those intermediate and product, involving main byproduct, carbon monoxide ($\ce{CO}$), which is believed to be poisoning the $\ce{Pt}$ electrode in most cases.
References:

R. Parsons, T. VanderNoot, “The oxidation of small organic molecules: A survey of recent fuel cell related research,” Journal of Electroanalytical Chemistry and Interfacial Electrochemistry 1988, 257(1–2), 9-45 (https://doi.org/10.1016/0022-0728(88)87028-1).
W. H. Koppenol, J. D. Rush, “Reduction Potential of the $\ce{CO2/CO2^{.-}}$ Couple. A Comparison with Other $\ce{C1}$ Radicals,” J. Phys. Chem. 1987, 91(16), 4429-4430 (DOI: 10.1021/j100300a045).
T. Iwasita, W. Vielstich, “On-line mass spectroscopy of volatile products during methanol oxidation at platinum in acid solutions,” Journal of Electroanalytical Chemistry and Interfacial Electrochemistry 1986, 201(2), 403-408 (https://doi.org/10.1016/0022-0728(86)80064-X).