Would anyone know about the CC/I-215 situation? I also don't know exactly how it came into being or how Clark County agreed to build it, nor do I know how CC-215 can become I-215 aside from being built up to standards.
You just gotta ask the right person...

The Las Vegas Beltway is not "county built, state maintained". There are two, slightly more than 2-mile sections, that are NDOT maintained (I-515 to Stephanie St, and Windmill Ln to I-15). I presume NDOT maintains those two sections because they had some stake in design and construction of those two sections and the associated Interstate interchanges on either end (NDOT did build the I-515 to Stephanie section as part the I-515 interchange reconstruction). The rest of the 215, including the portions signed I-215 between the two NDOT maintained sections, is maintained by Clark County.
The need for a beltway in the Las Vegas area I believe was identified in the 1980s. My understanding of the situation was that NDOT recognized the need (perhaps funded or took part in initial studies), but was not going to be able to fund planning and construction on their budgets. If there was the typical north/south or Vegas/rest-of-state political climate at the time (as is usually typical in most state matters), there was likely not enough statewide will to increase taxes or divert funds from other areas to move forward on a state-funded beltway in Las Vegas when the area was already receiving a significant chunk of transportation funds—this time period was during the initial boom of Vegas' major growth.
One of the main reasons Clark County was able to build the beltway was that county voters passed the "Question 10" tax initiative in 1990, which levied various taxes for various transportation/infrastructure improvements—one of the specific purposes of the county gas tax increase portion of that initiative was to fund construction of the beltway. (A new "Question 10" initiative was approved in the mid 2000s which extended/increased this funding.) If I recall correctly, since there would be no state or federal money involved, the county was also able to take advantage of a less-intensive FHWA environmental impact/review process (which might not be an option anymore) that allowed them to get the ball rolling much sooner than the state would have been able to. Former County Commissioner and Regional Transportation Commissioner Bruce Woodbury (for whom the beltway is now officially named) championed the Question 10 initiative and efforts to accelerate the beltway's construction.
So thus far, nearly all of the existing beltway has been funded and constructed by Clark County. The decision to initially build frontage roads and interim facilities along significant chunks of the beltway (in order to get some road in place earlier than building each freeway section one by one) was also made by the county.
It was always planned that the beltway would eventually be constructed to Interstate freeway standards and eventually fully signed as such. AASHTO approved the I-215 designation along the southern segment way back in 1993, before any of it had opened. An article responding to a reader's question in the Las Vegas Sun a few years ago stated that once the beltway is fully constructed to Interstate freeway standards, the whole 50+ miles will be re-signed as I-215 and would be transferred to NDOT maintenance and control. (If I had to guess, NDOT will probably relinquish to Clark County some/most/all of the arterial roads that are state highways within the urban county jurisdiction as part of this transfer.) State ownership is not a prerequisite for an Interstate designation, as about 2/3 of what is currently signed I-215 is owned and maintained by the county.
Yes, CC-215 and I-215 is 3/4 loop around Las Vegas, Northeast side were never being built. It was first started construction around 1994 as part of Las Vegas International Airport expansion project. The original segment was from I-15 to Windmill Parkway. I-15 interchange at I-215 was very different in 1994-97 like I-15 South going underneath I-15 fwy then going to I-215 East, I-215 West to going I-15 North. Look like it was sort of "Tropicana Bypass" going to Airport Connector tunnel to Las Vegas Internation Airport.
I'll try to interpret and expand on what this quote is saying...
The 215 is a 3/4 beltway, with the eastern segment not being planned or constructed (a feasibility study in the mid 2000s put a potential $1 billion price tag on an east leg, so the idea has been squashed).
The initial segment, I-15 to Windmill and including the airport connector/tunnel, opened in late 1994—I believe the airport connector project coincided with initial construction of the first two wings of the D-gate concourse at McCarran Airport (although I can't confirm). The general layout of the I-15 interchange hasn't changed much since original construction (aside from adding in 215 to the west and the recent I-15 widening), although the original segment did primarily just function as alternate access to the airport.