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:
[media]I would have expect that the feedback would be sent to the corresponding target of the execute command.
This may relate to MC-184419.
This is consistent with every other command. If commands did send feedback to the execute as target, it would spam players' chat with feedback in data packs, or command contraptions.
Absolutely by design.