New installation will overwrite old and all used components from online package manager need to be downloaded and installed again.
Is there a way to do that much easier?
There should be no need to download packages again (mostly).
If you haven't saved the downloaded files in the lazarus dir, that is => normally they go into the config dir, and that should be kept.
However, they will not be active after the Lazarus update. But Lazarus should still know them.
Go to menu: Tools > Rebuild Lazarus with profile ...
After that the IDE restarts, and packages should be pack.
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In rare cases, package are incompatible with the new version, then you need to download an upgrade for that package. (but between 3.0 or 3.x and 3.6 that is unlikely to happen)