When using locate or locatebiome commands via the execute command, the feedback is provided to the executor of execute regardless of the presence of the subcommand as.

Examples: execute the commands below through the server's console or a command block (replace <Player> by your player name).

execute as @p at @p run locatebiome lush_caves
execute as @a at @a run locate mineshaft
execute as <Player> at <Player> run locatebiome lush_caves

Each of these commands will provide feedback to either the server's console or the field "Previous Output" of the command block, but not the player:

I would have expect that the feedback would be sent to the corresponding target of the execute command.

This may relate to MC-184419.