Searching menu items - czech characters issue

This looks like it might be related to filter settings. The default (when nothing is specified in appsettings) is CaseSensitive=false, AccentSensitive=true. Which does not correspond to the behavior you describe. Did you change the settings? I think this should give you the behavior you want:

"ClientSortingAndFilteringConfig": {
	"CaseSensitive": "false",
	"AccentSensitive": "false"
},

Please note that the section name will probably change to “ClientFilteringConfig” because it does not have impact on sorting anymore.