I think it's useful to clarify terminology - the starlink antenna unit itself is the CPE. With my v1 starlink terminal you can plug literally anything into the PoE injector that is a 1500 MTU 1000BaseT DHCP client and it'll get an address and a default route out to the internet. All of the smarts happen in the antenna unit/phased array unit which also has its own fairly capable embedded CPU/RAM and routing capability.
The starlink indoor CPE, the home wifi router itself ,is a very basic thing that looks like something derived from a Taiwan ODM 802.11ac home router OpenWRT reference design with a custom firmware load.Or similar. If you've seen a teardown of one they're very simple.
With the v2 rectangular terminals it's similar but you need a cable adapter to go from the proprietary starlink cable to indoor unit, and additionally the indoor CPE unit also serves as the PoE injector.
In some other ISP type environments you might be expecting the indoor unit to be the CPE, such as what you'd get with a Comcast DOCSIS3.0 all-in-one modem+coax interface+router+wifi device attached to some coax coming in through a wall.