We live outside of DC and my kid got a local government/political internship that was advertised at their high school. Went through a normal interview process, no connections involved. I don’t think it’s necessarily impressive on its own, but it can help lead to other opportunities.

My current junior applied to a zillion simmer internships at federal agencies, companies, etc. She didn't hear a thing from any of them. She has top grades, course rigor, references and full time work experience (summer after freshman year). In retrospect it was a giant waste of time--both of hers and the teachers that she had wrote recs.
She ended up working full time and volunteering at a hospital (which was also a remarkably competitive process)

The only kids I know who got internships did so through family connections in private industry. I'm sure the federal ones come through for some kids, somewhere but it's probably 1:500 odds---someone gets them but it's not easy to be the one who is chosen.

My 11th grader has an internship through a contact she made through an extracurricular activity (not someone DH or I know).

Summer before senior year my child had a paid internship that was obtained through zero connections- just a regular application process. Precisely on par with with the kid wants to study.

Someone posted on another thread about a kid who had an interesting internship that may have helped with college admissions. Assuming we aren't just talking about direct connections made at that internship, it made me wonder what types of internships might be considered interesting or special re: college admissions. We are so fortunate to live in DC where the options are almost unlimited, so this just made me curious. FWIW my kids are still in MS so this isn't something we're even considering at this point, I'm truly just interested.