Without knowing what the interior drainage is now, it's not obvious that upgrading that will be of much benefit. If it's there, and water is coming through the walls, making more of it will probably not impact what's coming through the walls. If it's not actually defective/failed, replacing it seems like a probable waste of time & money.
The exterior solution you suggest is the way to be sure it's done and done, once.
If you want to take a staged approach, you could plan for an eventual (and possibly lower cost) curtain drain spaced away from the house by the width of your "roof", and do your "roof" and regrading, while leaving yourself clear markers for where the edge of the "roof" is so that you could trench and drain just beyond it if needed. Regrading and handling roof runoff correctly are major factors (your pictures do not imply a heavily sloped/hillside site, so odds seem good that most of the water is roof water.)
With a properly functioning drain, full of crushed stone and lined with filter fabric, the elasotmeric coating, et al are pretty much things that you do because you have the foundation exposed, rather than truly essential elements - if the drain is working, there should be no water pressure on the exterior side of the wall. That is the point of the drain. Placing the drain away form the house eliminates exposing the foundation, so you'd not do those things. If you are going to end up trenching by the foundation, you will be redoing all the work put into regrading and "roof."
As for the garage side, drain around the outside of the garage, below basement floor level, too. Assuming the garage is a slab, that one will definitely want to be spaced away from the garage so as not to undermine the soil loading of the slab.
you are going to have to dig it all out, and then rebuild it properly. you could shore it with steel plates, but it will cost you more to have the system built and then installed than it will to just do it over in concrete.
Best Answer
What your seeing is called efflorescence which are mineral deposits from moisture which sometimes seeps through exterior walls. Even though the basement walls may be inset from the main level water will migrate through soil layers. It appears that the other side of that wall is in contact with compacted soil. Even if it was water-proofed during construction moisture can sometimes seep through.
I don't think it looks serious. It would be different if water was obvious or pooling on the interior. At this point you can treat the interior walls with water-proofing material such as Drylok or Flex Seal. Although it might solve the efflorescence issue it won't keep moisture from seeping into the wall from the soil. The other option is to excavate the exterior of the wall and treat it with water-proofing which would be labor-intensive or prohibitively expensive.
As I indicated I would try to keep exterior groundwater away from the foundation and if the efflorescence is a major concern for you can treat the wall with an interior water-proofing product.
