Not a chemist but if you're comparing methane to refrigerants it doesn't even come close. Methane has a GWP of 27. That means it's 27 times worse than CO2. However, even the "environmentally friendly" HFO refrigerants like R-454a being used now have GWPs in the hundreds. If you look at the last gen of refrigerants like R-404a and R-410a which are still in use in most equipment you're looking at GWPs in the thousands and sometimes over ten thousand. Hell, just a few weeks ago I was working with R-508b which has a GWP of 13,396 and an atmospheric lifetime of 5,524 years.

The only common refrigerants you'll find which have a GWP near methane are the hydrocarbon refrigerants like R-290 aka propane. However those can only be used in small appliances due to the flamability concerns. It probably wouldn't be a great idea to have several hundred pounds of liquid propane coursing through the walls of a grocery store for example (especially with how bad many grocery stores leak). The gold standard though for environmentally friendly refrigeration is R-744 aka carbon dioxide. It has a GWP of 1 making it the most environmentally friendly common refrigerant out there. However right now it is only used in heavy commercial and industrial refrigeration due to the cost of equipment designed to operate at the pressures required to use it. Also CO2 has a nasty habit of going supercritical at temps most places regularly reach during the summer so R-744 systems need to be designed to operate as transcritical systems which also adds a ton of complexity and cost.