So I've had a 338 Spectre for years and used a few different 9mm suppressors with it without issues.
Got my new AAC Tirant 9 HD and wanted to use it with my 338 Spectre.

So I go to sight it in as a new suppressor could change piont of impact. First shot at 100 yards I couldn't see it on the target, so I fired a second round and it was just a little off and needing small adjustments. I like to have my guns set-up to shoot piont of aim piont of impact from cold bore shot.
So after letting gun cool down I wanted to check cold bore piont of impact and I've had something that has never happened before. The first shot will be 8" to 10" inches low and then all following shots will be dead on target. I did this several times with the same results.
All I can figure is that the gasses are effecting the tail of the projectiles differently between cold can with no previous hot gasses and one that is filled with hot gasses from being fired.

Info, Brand new AAC TI-RANT HD 9MM that I added a 3 lug adapter to.
I didn't bring my usual 9mm suppressor that I use with this gun thinking that I wouldn't need it. Guess I should have brought it.

I want to get a different mount for the new can and see if that would make a difference, but no idea if that will do anything.

First shot, cold bore shift when I see it is maybe 1 to 2 MOA with many rifle suppressors. This has been separate  from POI shift of unsuppressed versus suppressed. Sometimes the group size barely increases it’s just that the ‘flier’ in the group is almost always the first shot.

I just watched a YouTube video by Backfire, on this topic "cold bore" shots.
Interesting topic and need to experiment with it.

3-lug and precision should not be used in the same sentence.

I use 2 other 3 lug cans with this gun without issue and are very accurate.
But I get what you are saying. 3 lug can induce some impact shift.

I’ve stopped using 3-lug on 300 blackout because it opened up group size with long subsonics. Less so with supers. But supers heating things up faster can impact spring temper / tension in the 3-lug mount and I mostly shoot blackout supers. So I gave up on 3-lug for blackout. If something doesn’t work, or work well then there are enough alternatives to use.