Been in ID for 2 months now and have ID license...

Never been delayed in OR when I lived there, will I get delayed buying new gun in ID?

Depends, do you list your ssn when you fill out the form?  Do you have a concealed license?  How common is your name?  FYI, it's the same background check, your location is the only thing that has changed. Long gun or pistol?  Non-residents may purchase a rifle while visiting from out of state and walk out the door. If it's a pistol, it has to be transferred to an FFL in your state of residence.

Theoretically you should be fine, unless you have done something to warrant a red flag since your last purchase?

ETA, you have an Idaho license you are ok, if you had out of state license and tried to buy a handgun here they would have to transfer to OR dealer.   Also with a concealed license, you can skip the background check/phone call here in Idaho.

I had been in Idaho for less than a week when I waltzed into Sportsman's Warehouse with a paper license and picked up a Glock 43.

FWIW my brother is a LEO in ID and owned many guns before moving here. For whatever reason his first purchase in ID was delayed for a few days.

Even though is constitutional carry for residents, I'd suggest thinking about an ID enhanced cwp.  You'll have reciprocity with almost 40 other states, and no NICS check whey you buy a gun from a dealer.