This topic has been done to death.
In my experience those who do inform tend to be a little more authoritarian and tend to favor tighter restrictions on handgun permits.
Absent a legal requirement to do so, it’s ultimately your choice, do what works for you. I choose not to because IMO all it does is adds more time to the stop and gives the cop one more hassle to deal with.
In Colorado I am not required to inform the officer unless I am asked then I am required to surrender my permit w/ a valid ID. (CRS 18-12-204).
In Colorado my permit information is not tied to my driver’s license in anyway, the only way the cop is going to know I’m armed is if he sees it or asks me.
I don’t generally open carry. I have no objection; I just dress in a way that makes it impractical. If I am in my car my gun is generally on my right hip behind the seat belt I just don’t see the cop noticing it unless he has X-ray vision.
I carry my DL/registration/ proof of insurance in my wallet.
Bearing all that in mind this is how I handle a traffic stop.
As soon as the lights go on I take my wallet out of my pocket and have it in my hand I keep it in my hand until the stop is over, then I pull as far off the road as I can.
When that cop comes up to the car I have my hands in plain sight on the wheel w/ my wallet in my hand (no reaching for anything and giving the cop a chance to see my gun) I keep my wallet in my hand until the stop is over. I also turn the dome light on at night. IMO this negates the main rationale people give for informing, the cop isn’t going to notice my gun.
So, the cop asks for my papers I open the wallet, he can see everything I’m doing, and I hand him the documents and he does his thing and I’m on my way. No opportunity for him to notice any “suspicious bulges”. No reason for the cop to get nervous. No reason to prolong the stop.
If the cop asks me if I have any weapons in the car I say nothing and hand him my permit and go from there.
The only reason I would inform the cop w/out being asked is if he asked me to step out of the car.
In Colorado Springs that means I am almost certain to be patted down, so I hand him my permit before I get out of the car.
IMO “Showing respect” is nothing more than submissive urination, like a puppy that pees as soon as you touch it so you won’t beat it.