LSP4E does not provide a way to control space/tab insertion.
There were indentation problems in Visual Studio Code, this could be a common problem.
Bumping this issue. I'm experiencing this currently and my organization's Checkstyle configurations are not happy with me whenever I use Copilot. It should at least respect General -> Editors -> Text Editors -> Insert spaces for tabs.
A somewhat janky fix is to enable Java -> Editor -> Save Actions -> Format source code (Format edited lines) but this is very much a workaround and may have other annoying side effects that you might not want when editing your code.
At least some form of completion formatting is currently present in LSP4E need to add support on our side.