I had the exact same question some time ago - shortly after it went into effect. I spoke with my Sheriff, my ffl, the AG's office, and my state delegate.
Here's what I found out:
SB 353 make WV CCW permit "eligible" for exemption from the instacheck by bringing WV code more in line with federal requirements. However, it is still up to the Feds to grant the exemption for which our CCW permits are now eligible.
The AG (and Gov) should be the office(s) to petition the Feds/ATF for the exemption. Now that election season is over and WV has a new AG to be sworn in, WV residents should pressure incoming AG Morrisey to move forward with this. The previous AG was also pro-gun, but it just didn't get done in his term.
Sheriff tells me the bg check for CCW has not actually changed - only the code was tweaked to meet the eligibility standards. All counties should now offer a photo CCW, but some (like mine) will charge an extra $5 for the photo version. I still have the old style (no photo) but will get the new style when I renew next year.
Until the Feds grant the exemption for which we are now eligible, expect to go thru the instacheck when purchasing a firearm.
The above is to the best of my knowledge as learned from my inquiries. Accuracy is not guaranteed. Gary Slider is a member of this forum and is usually on top of these things. He may be able to chime in with further updates.