Does i.MX93 chipset support an internal RTC Controller? Will G50M SOM manage the battery and charge it?

Yes, RTC battery should be provided for RTC_PWR which can then be used by RTC controller on SOM.
G50M SOM will not support battery charging. A 2-pin header for CR2032 battery connection is available on the G50D carrier card for support.

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Please find the detailed G50M product information in the below link,