fix(Client): omit private properties from toJSON

[SpaceEEC]

Please describe the changes this PR makes and why it should be merged:

This PR changes Client#toJSON (and BaseClient#toJSON) to

• Remove references to properties that are either no longer on the class or won't get included in the resulting json anyway
• Are private (and cause an error due to indefinitely recursing) and shouldn't be included in the resulting json

Status and versioning classification:

• Code changes have been tested against the Discord API, or there are no code changes
• I know how to update typings and have done so, or typings don't need updating

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1 Ignored Deployment

Name	Status	Preview	Updated
discord-js	⬜️ Ignored (Inspect)		Jul 22, 2022 at 3:00PM (UTC)