Well, based on my brief search, there aren't any aftermarket headlight housings available for a 2013 RDX that incorporate higher output optics/emitters. (Option 4.) As such, you're limited to the factory housings or aftermarket housings that are similar in type to factory, with bulbs that are similar in type (Halogen vs LED vs HID) that came in them from the factory. Your housings have a SAE/DOT stamp on them stating that they are designed/approved for the type of bulbs that came in them from the factory.
I'll be as helpful as I can. Stay away from the amazon LED drop-in units. I know, "but how can Amazon sell something that isn't legal for my car." Well, first Amazon is in the business of selling cheap junk, and second that's why the listings all say (or should) "for off road use."
Don't despair. There are safe/legal/approved/effective options -
0) New bulbs. Halogen bulbs decrease in output over time. Often OE bulbs are a LL (long life) spec which sacrifices output for life. Don't go to the parts store and get the Ultra, "Blue" or "Laser" marketed models. Fresh bulbs might be the ticket. If you lived near me, we'd start here. I have a drawer of bulbs from various experiments.
1) Aim. If your low beams aren't aimed right, putting most of their energy into the air, you'll be at a disadvantage.
2) A new set of housings might perform better if your current reflectors/optics/housings are degraded. TYC housings are often a pretty good product at better than OE pricing.
3) If housings are in good shape, for some halogens, there are "like kind" bulb upgrades that can get extra output. A H9 can be changed safely for a H11 in some applications. 9012 for 9006. 9011 for 9005...often while preserving proper patterns without increasing glare or heat. Often their is a bulb life decrease associated with going this route but it's cheaper than a new car or accident due to poor visibility.
4) Aftermarket - for some cars there are viable aftermarket housings available that integrate better optics (projectors) and sources (LED or HID.) Some are just for show but there are instances where aftermarket > OE. In this case, the manufacturer should be one that certifies their housings to SAE/DOT requirements. Morimoto and AlphaRex are two that come to mind but I don't see any options for a 2013 RDX.
You can't just slap HID or LED bulbs into a fixture that is legally approved by SAE/DOT (and stamped) for halogens and expect improvements or legality.
Specifics: 2013 RDX is not an atrociously expensive housing. Looks like a single beam halogen projector low (H11 bulb) and a halogen reflector high (9005 bulb). If the housings are in good shape, I can guarantee a set of H9 bulbs in the lows and a set of Toshiba 9011 bulbs in the highs would change your world for well under $75. (Minor trimming of the bulb tabs is necessary, but easy. I've done both conversions before.) You'd probably only get 2-3 years out of the H9 lows, so I'd keep an extra pair ($25) in the glovebox. I'd polish the covers for good measure and repeat annually. If they aren't too bad toothpaste is sufficient.
H9: The Philips "standard" model is class leading, $11 each on amazon.
9011: The Toshiba model is class leading, ebay, <$20 each delivered. Also search via Toyota PN 90981-13066.
The Japanese projector optics from that era aren't amazingly efficient but if they're in good shape, they shouldn't be a problem. My 2009 toyota projectors (factory) still have good life in them but I have to stay on top of keeping the lenses clear. They've been garage kept and aren't terribly UV damaged for being 15 years old.
The projectors on my commuter car were tired H11 bulbs (like yours) and the H9 conversion was incredibly effective, probably yielded 75% additional light output. Shortly after I swapped, I got a pair of new TYC housings due to a deer plowing event. Retiring the 10 year old factory units, which also helped.
H11 to H9 conversion info is easy to source on the interwebs:
https://www.candlepowerforums.com/threads/difference-between-h9-and-h11-bulbs.254193/ With the additional output comes additional reponsibility - make sure the cutoff is aimed below the horizontal.