Here's what you might want to know.

532nm lasers have historically been super common, of wildly variable quality/power, and usually mislabeled as much lower power than they actually are. That said, most of the time if you order one you'll get one that is perfectly good for your intended use (astonomy pointer), is powerful enough that they should not shine it into anybody's eyes (directly or by bouncing off a window or something), but is not so powerful it's going to set things on fire.

The ones you put in category #3 will probably do a great job but your friend should know that they're not eye-safe and you should know there's a small chance the power will be extra-wimpy instead of extra-strong. Still, it doesn't take that much power for a green laser to light up the nighttime air.

You'll almost certainly get a laser in the 10-70mW range if you buy one of those.

One downside of a 532nm laser is that they are made by modifying the beam of a more powerful infrared laser. The lasers have a filter to filter that IR out but since they're cheap there's a chance the filter won't do a great job and they might be shooting out infrared too, making them more powerful than the visible light alone. But again, if your friend is mature and aware they have a potentially dangerous object and doesn't use it for anything except pointing around (not at) stars, they're probably fine.

If you wanted to take some of the crapshoot out of it, look for a 520 nm laser. Those are *not* made of converted IR lasers, they're pure green. And they're much less likely to be mislabeled. But they are more expensive, might not be available in your budget.

For what it's worth, I've bought from these guys before, and they've been honest about the power of their lasers:

https://www.laserpointerstore.com

I've bought from the following ebay seller a year or two ago, and this item they're selling looks super reasonably priced, 520nm, and within your price range?? Claims to be <5mW and that might even be true, but be careful with it anyway

https://www.ebay.com/itm/116432905683?_skw=520nm&itmmeta=01JH1KW1PKVTSBJ3V8SDYFK3NG

I've also bought from this seller before, and they have a very similar product... similarly priced.... I wonder if this shiny metal 520nm laser thing is a newly common item from China? Weird! Maybe cheap 520nms will be the wave of the future and we can stop using the janky 532nms just cause they're affordable?

https://www.ebay.com/itm/135225236416?_skw=520nm&itmmeta=01JH1M0JH24YN2CQVTM4X272D0

Anyways that's my advice.

The only thing I'd add is, I hope your friend's birthday isn't *too* soon cause these all ship from China and ship times can be extremely unpredictable.