Would a ledge vanity work?

The first one looks to be a pair of cabinets, with a top attached. The second one is a Cerastyle sink. https://www.thebathoutlet.com/bathroom-sink-rectangular-white-ceramic-wall-mounted-or-drop-in-sink-cerastyle-081000-u/product/2217

Any local cabinet shop will have zillions of styles and combinations.

My parents had a custom Corian top with sink cut to fit over two banks of drawers at either side to create a vanity that worked for my dad, who used a wheelchair. It's an older remodel, but it worked beautifully and could be adapted to any style you prefer. I'll try to grab a pic when I'm next over there.

Additional considerations: If the vanity will be used by someone seated in a wheelchair or other chair, be sure the mirror comes down far enough to be useful and consider using medicine cabinets on adjacent walls, rather than behind the sink, so they can be reached. It makes sense to measure what actually works for the person concerned in the space at hand, rather than using generic ADA measurements.

I am in the middle of doing a combination standing and rollator walker/wheelchair friendly bathroom remodel. We are gutting our small bathroom and stealing a foot from the adjoining bedroom just to get the room to have a deep enough shower and get rid of the protruding wall at the end of the tub that makes maneuvering in the bathroom so difficult.

I found some wheelchair accessible vanities that met all the ADA specs. They cost a fortune and have little storage. The ones I liked best were Lacava, and they can cost up to several thousand dollars for the largest ones (once you also get their top). Here are the Lacava vanities, click on them to see more.

Because I don't yet need a wheelchair, but my knees will "go out" on me, I will sometimes grab a counter and use it to hold my weight until my knee pops back in place. So none of the wall-hung ones would be good for me for that reason.

Simply googling "ADA bathroom vanities" gets a number of selections. Many of the ones you get in a search suffer from the same problems as the ones people have posted here - no room for the wheelchair footrests with the person's legs on them, not enough room for someone to approach the sink at an angle and needs to be approached head-on when there is not enough room in the bathroom to do that, or just plain misunderstanding of what a wheelchair user might need. But there are a few.

Four ADA vanities on Houzz.

This one gives pictures of some nice ones, all wall-hung. If you look through modern vanity lines, especially those from Europe like Duravit, Lacava, Nameeks, you will find wall-hung cabinets, and some are a single drawer deep, so they may work in your case. Or there are a few that have the sink to the side by itself and the drawers on the other side, like the one of the four linked above. The website AllModern.com has some of the less expensive wall-hung modern vanities. I have no idea of their quality, though.

Another option is always a larger console sink with brass legs. The ones with two sinks give you more maneuvering room. Here is one with a sink and a counter:

One big sink - and ADA compliant on heights and distances and everything:

This one is supposed to be ADA compliant, but I would not want to try to reach that sink from a wheelchair, I would much prefer the sinks that protrude out past the counter. Try clicking on the picture, it might take you to the page to see the rest of the pictures and you can see what I am talking about. It is a simple undermounted sink about three inches in from the front edge. I guess it is not all that much further than the console sinks I posted.
I had also considered getting a piece of furniture shaped like a console and having it made into my vanity. There is this glamorous mirrored console on Chairish.com that is just the size I need that I considered sending for. Until I remembered that it is covered in mirrors. Glass. Breakable, I throw my walker around like a crazy person! That one seems to have sold, but here is one just the right size to make into a sink console, if you need one around 48" wide. $500 if you are in Alameda, California. Another few hundred to ship it, depending on where you live. You could put a sink where the middle drawer is and still have two drawers left to use. I bet you could find the right sized sink at Duravit. You can get stone or glass to cover the top.

The console at Chairish.com

Check Craigslist in cities near you for "Consoles" and see what you find.

Looking at the two examples you give, the first is a simple pair of two drawer bases with some clever carpentry work between them to make the board behind the sink's lip and the slanted board in the knee hole. You can also buy a used desk, if you find one with a big enough knee hole. Just take the center drawer out and rig a way to hold the drawer front in place as if it were still there. Craigslist is also a good place for desks. Chairish is a good place to find very nice used furniture and antiques. I have gotten some 1950s end tables there.

I was going to use an antique lady's vanity for my bathroom, until I sprained my knee this summer and learned how much room my rollator needs. I am trying to keep my counter top down to 12" to 15" and the sink will then come out past it several inches. My vanity was 18", so now I am going to have to sell it. My carpenter/contractor who does the bathroom remodel for me is going to make me a narrow vanity and I will order the drawer boxes from Barkerdoor.com once he has the sizes figured out. We will cover it with a commercial-grade laminate in a metallic silver that looks good with the man-made quartz counter top I am committed to using.

The second sink you show is a wall-hung sink. I will do a quick search, but you may want to do a look-see at all of the ones available because they are so nice. Try a couple of sites, like qualitybath.com as well as Build.com to look at sinks. I did look at Build.com for a few minutes and did not see that exact sink. American Standard has one with a rounded front and "wings" on the side like that.

This may be your wall sink. It is by Laufen and costs $900, and it looks pretty close.Laufen sink.

Scarabeo, a Nameeks company, does a wall-hung counter-plus sink for $574. It has a small counter on one side of the sink and a really big one on the other. If you look at the sink before this one, it switches the sink to the left side. Scarabeo 36 inch wide wall hung sink.

This Nameeks GSI Panorama 31.5 inch wide sink is $481 plus $120 if you want a towel rail on one side.

It is worth it for you to look at the actual ADA sinks at the Build.com site. They are less expensive than a lot of these sinks, and the one I looked at by American Standard said that they made it out of extra-thick porcelain. It cost in the mid $200 range. Kohler also had them, for about $75 more. Theirs have a curved front that would make it very easy for someone in a wheelchair to get close to wash or brush teeth.

When you get going, if you need any more help finding sinks, let me know. The ones that stick out beyond the edge of the counter are called Semi-Recessed. I have scoped out the sinks like this and have many of them saved in pictures or or in a data file. Duravit makes a lot of them. Theirs also come in smaller sizes and smaller prices. They also have a special finish that it is probably worth getting, called WonderGliss. It costs an extra $50 or so, and adds two months to the time to get the sink, though. Quality Bath has most of the sinks I saved. BTW, they close their website Friday dusk to Saturday dusk for the Sabbath.