When you summon a new entity with a translated name and you select that entity by name, the selection is not the same in 2 different languages.

Example:

• Select English (US) in language settings.
• /summon minecraft:cow ~ ~ ~ {CustomName:" {\"translate\":\"entity.minecraft.chicken\"}

  "

Test:

• /say @e[name=Chicken] Result: [Mondemen] Chicken // It probably works
• /say @e[name=Poule] Result: [Mondemen] // It's normal

Now if you change the language to French and you retry the previous commands:

• /say @e[name=Chicken] Result: [Mondemen] // No selection
• /say @e[name=Poule] Result: [Mondemen] Poule // Selection

Normally and logically, I think that in this case, it will only be necessary to test the name of the translation, not the value.

In addition, the translations are only client-side, non-server, does it mean that the server retrieves client translations?

It's not very clear.