Replace string-typed file paths with `PathBuf` / `impl AsRef<Path>`

[emlautarom1]

Description

Several public and internal APIs represent filesystem paths as String / &str / impl AsRef<str> instead of the idiomatic std::path::PathBuf or impl AsRef<Path>. This leads to:

• Lossy conversions (.to_string_lossy()) when the two representations must be bridged.
• String concatenation used to build paths (format!("{dir}/{prefix}.json")) instead of Path::join, which is not cross-platform and bypasses the type system.
• Error messages that store paths as String, losing structural information.

All occurrences should be migrated to PathBuf (owned) or impl AsRef<Path> (borrowed generic), consistent with the Rust standard library conventions.

Affected locations

crates/dkg/src/disk.rs

Location	Issue
Struct field Config::def_file: String	Should be PathBuf
Struct field Config::data_dir: String	Should be PathBuf
write_lock(data_dir: impl AsRef<str>, …) (≈ line 207)	Parameter should be impl AsRef<Path>
check_writes(data_dir: impl AsRef<str>) (≈ line 285)	Parameter should be impl AsRef<Path>
keys_dir.to_string_lossy().to_owned() (≈ line 190)	Lossy PathBuf → String conversion; downstream API is the root cause

crates/dkg/src/dkg.rs

Location	Issue
Struct field Config::def_file: String	Should be PathBuf
Struct field Config::data_dir: String	Should be PathBuf

crates/eth2util/src/keystore/store.rs

Location	Issue
store_keys(…, dir: impl AsRef<str>) (≈ line 60)	Should be impl AsRef<Path>
store_keys_insecure(…, dir: impl AsRef<str>, …) (≈ line 42)	Should be impl AsRef<Path>
store_keys_internal(…, dir: impl AsRef<str>, …) (≈ line 65)	Should be impl AsRef<Path>
load_password(key_file: impl AsRef<str>) (≈ line 158)	Should be impl AsRef<Path>
store_password(key_file: impl AsRef<str>, …) (≈ line 175)	Should be impl AsRef<Path>
check_dir(dir: impl AsRef<str>) (≈ line 189)	Should be impl AsRef<Path>
write_file(path: impl AsRef<str>, …) (≈ line 220)	Should be impl AsRef<Path>
format!("{dir}/{prefix}{i}.json") (≈ line 78)	Use Path::join instead

crates/eth2util/src/keystore/load.rs

Location	Issue
load_files_unordered(dir: impl AsRef<str>) (≈ line 81)	Should be impl AsRef<Path>
load_files_recursively(dir: impl AsRef<str>) (≈ line 130)	Should be impl AsRef<Path>
extract_file_index(filename: impl AsRef<str>) (≈ line 257)	Should be impl AsRef<Path>

crates/eth2util/src/keystore/error.rs

Location	Issue
DirNotExist { path: String } (≈ line 10)	Should be PathBuf
NotADirectory { path: String } (≈ line 17)	Should be PathBuf
PasswordNotFound { path: String } (≈ line 28)	Should be PathBuf
KeystoreNotFound { path: String } (≈ line 123)	Should be PathBuf

crates/cli/src/commands/relay.rs

Location	Issue
RelayLogFlags::log_output_path: String (≈ line 272)	Should be PathBuf

Acceptance criteria

• All struct fields that represent filesystem paths use PathBuf.
• All function/method parameters that receive filesystem paths accept impl AsRef<Path>.
• No .to_string_lossy() calls on paths that are immediately passed into another API.
• Path construction uses Path::join / PathBuf::push instead of format! string concatenation.
• Existing tests continue to pass (cargo test --workspace --all-features).
• No new clippy warnings (cargo clippy --workspace --all-targets --all-features -- -D warnings).