`LanguageServerSeed` is used as a key to identify language servers.
Previously, it included the entire `LspSettings`, which meant that
changing `lsp.<server>.settings` (dynamic configuration) would cause the
server to restart unnecessarily.

Dynamic settings can be updated via LSP's
`workspace/didChangeConfiguration` notification without requiring a
server restart. Only `binary` and `initialization_options` should be
part of the server identity, as changes to these genuinely require
restarting the server.

This is a follow-up fix to #35270 which introduced `LanguageServerSeed`
but inadvertently included dynamic settings in the server identity
(although I remember that this dynamic settings reflection stopped
working pretty recently, so there might be other commits besides #35270
that changed the behavior of `LanguageServerSeed`)

Closes #ISSUE

Release Notes:

- Fixed language servers unnecessarily restarting when changing
`lsp.<server>.settings` configuration. Dynamic settings are now properly
updated via `workspace/didChangeConfiguration` without requiring a
server restart.