Does the Columbia Basin, North Cascades and Idaho Panhandle/Clearwater get a lot of violent, rotating supercellular thunderstorms?
Note: These inputs are of a meteorologist who has quite actively tracked severe
weather around the US for a couple
decades... but also hadn't spent as much time in or attention on the west and northwest of the country.  So there could could theoretically be some degree of unintended bias.  I've tried to use objective data where possible, but it's something to keep in mind, regardless.

In terms of &quot;a lot&quot;, at least for tornadoes/hail, I'd suggest that nowhere west of the Rockies sees a lot truly:


Tornadoes [left], hail [right]... source: Storm Prediction Center SVRGIS page
I'd offer the idea that there of perhaps two notable reasons for that:

The lack of consistent and widespread surface wind fields favorable to tornadoes... due to a combination of the lack of the big lee cyclogenesis seen east of the Rockies, along with the complex topography.
The rarity of regular low-level moisture significant enough to allow for low LCLs.  The higher the storm base is above the ground, the less likely a tornado
[in figure 6 of Edwards and Thompson 2000, all the red boxes showing tornadoes are on the left side, which are lower LCLs]

The lack of rich low-level moisture is due in large part to the lack of accessibility from warmer moisture sources, particularly the Gulf of Mexico; the Rockies provide a barrier to much of the moisture reaching further west.
As you note, parts of Wyoming and Montana do see supercells and tornadoes a bit more often... but on a good topographic map, fair parts of those states are east of the Continental Divide, and so still on an &quot;upsloping&quot; area and thereby not blocked by sinking regions which prevent full moisture progress.  They're still less-tornado prone due to elevation and increased distance from moisture, but it does happen.
The desert southwest also does manage to get monsoon moisture sneaking around the terrain further south... but further north that monsoon moisture sees additional blocking by the more elevated terrain across Nevada and Utah.  (And in the southwest, a different key ingredient in tornadic supercell development is typically missing in the summer monsoon: upper-air winds sufficient for supercell development)
The Pacific Coast does see a few occasional tornadoes.  But from what I've seen, they typically form from smaller storms with much less classical and intense mesocyclones.  As you mention, they're a bit more in line with cold-core setups, which usually produce weaker short-lived tornadoes than classic supercells of the Plains and on east.  If you plug in the events you speak of into SPCs Severe Weather Events archive, [pick the date, then click Obs and Mesoanalysis on the left, then use the dropdowns to find various parameters]
you can see that CAPE was typically very meager (well short of 1000 J/kg) and the storm structure quite weak in reflectivity in comparison to a classic supercell, more indicative of such cold-core setups.
Capping inversions may be helpful to &quot;keep the lid on the pot&quot; if you have strong CAPE (and therefore quality moisture) and intense updrafts to erode the cap during the day.  But as it is, there isn't enough moisture typically for the cap to be a positive factor.
Quite a bit of the area you mentioned, such as Spokane, makes up one of the more arid regions of the country.  Further removed from the rain shadow of the Cascades, the Idaho Panhandle does get more precipitation, but it's mostly in cooler months that lack the deep convective development needed for supercells, probably because of the proximity of the Pacific high in summer months.  Further east in E ID/W MT, particularly in the Flathead Valley, there are occasional summer thunderstorms... but the storms may well be higher based due to the limited low-level moisture, and so have low potential of tornadic development.  For more on the climate complexities at play in the Idaho vicinity, check out this article from the Western Regional Climate Center.
In the end, the area you ask about is one of the weakest regions for supercell development in the entire United States.  The entire quarter of the country west of the Rockies isn't much better.  This page from Iowa State University will create an image showing the number of days since each pocket of the country (sorted by National Weather Service forecast office areas) last saw a tornado warning.  It shows that the Idaho Panhandle hasn't seen a tornado warning in over 10 years:

More than anywhere but northern California.
And another ISU page allows it to be shown that:

... Most spots in northern Idaho only see about one severe thunderstorm warning per year on average (versus 10-20 per year over Oklahoma).
So the danger of severe convective weather is remarkably low in that region of the country overall.