I find it embarrassing when someone says "Thank you for you service," or any of the other stuff.
I didn't serve. My dad did in WWII.
I grew up near a couple three military bases. Seeing and interacting with enlisted and veterans and their family and my family who served was an every day thing so it seemed normal to me and nothing special. VFW, VA all that stuff was landmarks that got referenced in everyday life when giving people directions.
Point being, like you, I never thought of it as anything "special" back then. Didn't not appreciate it but kinda took it for granted that this is what America is like.
Then I moved away and discovered it's not the norm. In some ways that's sad because a lot of people have no appreciation for the sacrifice even if just in lifestyle and even if it was voluntary. In turn, a lot of those people have no appreciation for America.
When I meet someone and learn they served, depending on how they react to it, I will sometimes offer them a "thanks" and quick handshake and leave it at that. If they engage more I reciprocate, maybe even ask them if they were a crayon eater or a wingnut or a squid.
If I spot a Vet, especially an old timer, at a coffee shop or restaurant sometimes I'll grab the waitress and quietly pay the bill before I leave. I hope they take it in the spirit it's given. Some people who served aren't that hard to spot. Not in a bad way, they just stand out from the "normies" like me.