You cannot choose which Favicon is preferred when the browser needs to choose among several. Each browser has its own implementation and as suggested by Robert Longso your only solution is to directly contact each browsers to check if it is the expected behavior.

For instance here are the rules for Safari browsers using apple-touch-icon: https://developer.apple.com/library/archive/documentation/AppleApplications/Reference/SafariWebContent/ConfiguringWebApplications/ConfiguringWebApplications.html#//apple_ref/doc/uid/TP40002051-CH3-SW4.