Subsequent Events - Preferred Stock (Details)	Jun. 30, 2026
Redeemable Convertible Preferred Stock
Redeemable Noncontrolling Interest, Carrying Amount
Temporary equity, cumulative paid-in-kind dividends, rate, subject to increase, common stock not listed on national securities exchange within 18 months, increase, percentage (as a percent)	2.00%

Temporary Equity, Cumulative Paid-in-Kind Dividends, Rate, Subject to Increase, Common Stock Not Listed on National Securities Exchange within 18 Months, Increase, Percentage

No definition available.

Name:	cgeh_TemporaryEquityCumulativePaidInKindDividendsRateSubjectToIncreaseCommonStockNotListedOnNationalSecuritiesExchangeWithin18MonthsIncreasePercentage
Namespace Prefix:	cgeh_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant