I think this will ultimately be solved by 3rd party clients.
There are tons of mobile apps in the pipeline and some already released. I just got set up with Memmy a couple days ago and it already makes things a bit easier; a step in the right direction.
On desktop I imagine browser plugins helping to tie the experience a bit more together. Hopefully the vanilla UI can also deal with cross-instance behaviour down the road.
The data that you entered into lemmy is stored: username, password, email (optionally), posts, comments, etc. Assume instances keep logs of all the API requests they get from any given IP. This is the case with nearly every website.
If you don’t provide email and lurk then I don’t see much of a concern. You can always use a VPN if you want more anonymity.