There is no mandatory requirement for law enforcement agencies to be trained on, or even given familiarity with, the Law Enforcement Officers Safety Act (LEOSA).

Due to that, there have been a number of individuals, properly credentialed under LEOSA and complying with the applicable restrictions, who were arrested and charged with violations of local/state gun laws because the police officers and the prosecutor didn't understand the law and/or thought that the state's law for concealed carry permits took precedence.

Most of those arrests/prosecutions occurred in the first few years following the passage of LEOSA in 2004. Since then, most have occured because individuals (such as Department of Correction employees) didn't "fit the mold" of a "retired law enforcement officer".

In other words, LEOSA won't keep you from being arrested, but will serve as an affirmative defense if prosecuted (the same as a "stand your ground" law wouldn't prevent you from being arrested, but would serve as an affirmative defense if prosecuted).

In all cases where the individual was properly carrying a concealed firearm under LEOSA, the arrest and/or charge was eventually overturned. As recently as 2022, the state of New Jersey would not fully honor LEOSA and imposed its own permit restrictions and/or interpretations of the impact of LEOSA on the state. The most egregious example was in 2018 where a prison guard received a five-year sentence in New Jersey for a gun conviction. The conviction was overturned, but the individual had already served three of the five years sentence (New Jersey v. Dana Johnson*)

What does all this mean, specifically in regards to your question. Recognition of LEOSA appears to be hit or miss. While most LEOs have a passing familiarity with it, many do not understand it fully so you should expect the officer to have some confusion, even on what they should do under the law (e.g., the differences under 18 U.S.C. between currently serving law enforcement personnel those that are separated/retired).

The NRA Law Enforcement Division* and the Fraternal Order of Police* recommend that you fully read through and adhere to all the requirements of LEOSA and, even though it isn't required under LEOSA, obtain a state issued carry permit if possible.
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* State of New Jersey v. Dana R. Johnson - https://cases.justia.com/new-jersey/appellate-division-unpublished/2022-a-5622-18.pdf
* NRA Law Enforcement Division - https://le.nra.org/understanding-leosa/
* Fraternal Order of Police - Information on the Law Enforcement Officers' Safety Act (LEOSA) - https://fop.net/government-and-media-affairs/legislative-resources/hr218-leosa/

Reference:
* LEOSA - Army - https://leosaarmy.com/
* DoDI 5525.12, "Implementation of the Law Enforcement Officers Safety Act" - https://www.esd.whs.mil/Portals/54/Documents/DD/issuances/dodi/552512p.pdf
* 18 U.S. Code, Chapter 44, Section 926C - Carrying of concealed firearms by qualified retired law enforcement officers - https://www.law.cornell.edu/uscode/text/18/926C

I imagine law enforcement wouldn't be confused by it since it concerns law enforcement. I haven't had to show anything other than my driver's license and I was very young when I did. Wish I could be more helpful.

Pennsylvania Issues An LEOSA Permit To Former And Retired Police And Corrections Officers.
I Have Maintained What Is Called Act 235 Certification , Special Police Officer Certification.
I Also Have Concealed Carry Permits Issued From Multiple States That I Travel To On A Regular Basis So I Can Legally Carry In Any Of The States That Recognize Other States Permits.