Migrate TypeScript `private` members to ECMAScript `#` private fields

Description

Standardize class member privacy on ECMAScript # private fields instead of the TypeScript private keyword. # fields are enforced at runtime by the JS engine (not erased at compile time), aren't enumerable, and can't be reached via bracket access — so the privacy guarantee is real rather than type-check-only.

src/utils/testing/persistence.ts already uses # fields. This issue brings the rest of the codebase in line with that convention.

Scope

Member declarations currently using private (≈7 across 3 files):

• packages/graph-explorer/src/utils/testing/DbState.ts — private _activeSchema
• packages/graph-explorer/src/utils/rdf/PrefixLookup.ts — private readonly userMap, private readonly inferredMap, private constructor
• packages/graph-explorer/src/connector/LoggerConnector.ts — private readonly _baseUrl, private readonly _clientLogger, private _sendLog

Also drop the _ name-prefix convention on members that become # (the # already signals privacy).

Caveats / out of scope

• private constructor (PrefixLookup.ts) has no # equivalent — JS has no private constructors. Leave it as private, or address the singleton pattern separately.
• readonly can't be combined with # fields in TypeScript. Migrating private readonly → # loses the compile-time readonly guarantee. Decide per-field whether runtime privacy outweighs losing readonly, or leave those as private readonly.
• Constructor parameter properties (constructor(private x …)) have no # shorthand and would need a manual field + assignment.

Acceptance criteria

• private/protected member declarations migrated to # where a faithful equivalent exists
• Fields where # would lose readonly or hit the constructor caveats are either left as-is or explicitly converted with the tradeoff noted
• pnpm checks and pnpm test pass

Related: #1830

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