Here in Portugal, most display useful info like date, time, outside temperature (with varying degrees of accuracy), as well as services provided by the pharmacy or some general (often season specific) health recommendation.

The use of a bright green sign is, of course, to seek attention, but it’s also useful to quickly spot an open place at night, when most are closed and only a few remain opened longer in each town/city neighborhood (called “farmácias de serviço”, i.e something like “pharmacies in service”; they usually rotate between themselves each week). Nowadays you can check which places are available at night through a nice website, but the signs remain a useful thing, nonetheless.

The animations are just a culture thing now, I’d guess. Different pharmacies employ different animations, some wackier, some less, though there are very common animations for sure, such as the one where a 3D cross is animated rotating on multiple axis at the same time, making a nice spin back to its original position.
Why? I dunno, they break up the usual info display and help grab attention? I dunno, you get used to it and it mostly gets filtered into the background hehe

That’s fucking annoying to look at.

“annoying” is the “made you look” of advertising.

I mean, the lit-up signs are for visibility. In some countries pharmacies are assigned strict working hours by the government, so it’s useful to see at a glance if a pharmacy is currently open without having to walk right up to the door (and night shifts may require ringing a bell in some of them, so that’s also helpful to convey that they are in fact open).

The fancy animations are just because when signs went from neon-lit to LEDs it turned out not all pharmacists have good design sensibilities. At least as far as I can tell.

Because they’re easy to recognize and consistent? It’s honestly more weird that other areas of the world haven’t followed suit.

You’re missing out, those are the tamer ones these days. https://youtu.be/x6Alv2Z347c?si=c_a2IkCBLB4AL4zo

A compilation in reddit: https://www.reddit.com/r/musichaiku/comments/153qvqo/pharmacies_in_europe_and_their_rave_signs/

Ok, so this might be an americanism, but the green cross says “cannabis dispensary” to me. At least around me, the medical marijuana industry is somewhat separated from the medical industry, and dispensaries are entirely different establishments from pharmacies. Pharmacies (and other medical establishments) use different symbols. If they were to use a cross to indicate a medical establishment, the red cross would be recognizable as a generalized symbol, but apparently it’s heavily protected by the Red Cross.

But that’s just my context, so I don’t have much of an answer beyond “this is what it means 'round these parts”

Edit: added info from below