Beginner choosing amp help

I would like to gain more detail/ clarity and more dynamics if possible without being harsh/ fatiguing. I’d like to stay in the 3 k range. I listen to 60% jazz and acoustic and a little bit of everything else. Mostly stream tidal

As far as source for streaming I’ve just been using my laptop plugging it into the usb directly on the Yamaha. I’m a complete beginner to this so I’m sure there’s a better way  for higher quality/ better resolution

Keep your Yamaha A-S801 and apply your budget to your source / streaming. You will get what you are looking for.

A "better" integrated driven by your current setup is equivalent to putting the cart before the horse. You will also be surprised at how competent and good your Yamaha is.

Once you have a good front end, you can move downstream for upgrades as your financials dictate.

Look into the LUMIN T2 or other similar products. 

Look at the Peachtree Nova 300 or 500 one of the sweetest integrated amps out there with a great built in DAC, USB and optical ins and a potent 300wpc.
https://www.themasterswitch.com/review-peachtree-audio-nova300
I bought one last year and it has changed how I listen to music.
It would be a great match for your Martin/Logans

look into a used integrated McIntosh.  

I went through valve amps, SS amps etc. and did a ton of A-B comparisons with my Wife and Daughter. They have bat ears and will notice even subtle changes in a system. Plus they knew/understood zero about the hardware. No hardware bias. And after testing much more expensive and highly recommended hardware, I was shocked that the clear winner was the Lyngdorf 2170. Had a tough time sending back the LTA hardware. It was so cool looking! Alas... So I put my money where our opinions were and purchased a 2170. It does remarkable things with both digital and analog signal paths. The best digital sound I’ve ever heard with some fairly expensive hardware upstream. But I wasn’t expecting the Analog to be so good. I feed it from a Feikert Turntable/Origin Live arm/Hanna SL cart/Whest two.2 phono pre. Now if you like the "tube sound" it may not be for you. But if you want the amp to disappear in your signal path, it will do that. It will also disappear in you room. It is a small amp if you’re not to the big house stage in your life yet.
The 2170 is closer to the $4K range in price but if you consider it includes an excellent D/A converter internally, and very effective room correction system, it may be more attractive. You can get them for less from some dealers. PM me if interested and I can give you a good source.

Big difference between the A-S801 and the A-S1100, A-S2100 and A-S3000. Fantastic phono stages and all three are about the same. For me the best deal is the A-S2100. Cant see ever selling it. Check out the reviews post, mags, digital trends and new record day. All I want to do is just keep up grading speakers and components.