I would not be happy with it.

Here's a side pic of one. Thought is an I-beam?

The rust and handprints are non-issues. You've paid one engineer; that's enough.

" Thought is an I-beam? "

It is but it is used vertically as a post. A beam is typically used horizontally.

The cracked portions of the concrete foundation should have been corrected by using injection ports and filled with epoxy and then the stitching method with carbon fiber staples. Here is an example to give you an idea.

The steel beams they installed have space between the beam and the foundation... that gap should be solid grouted with non-shrink mortar to provide full support for the wall, and the way they installed them, with blocking nailed, its odd, if you go to finish a basement that will be in the way, steel beam is attached to the inside of the joists and some have tension adjustment brackets welded to the column at the top.

Not sure on what the existing condition was prior to work, or the scope of work beyond the braces and crack filling, but:

- Permits: Typically you do not need a permit to do repairs. Unless specifically addressed by your building department, I would lean towards this work not needing a permit. Permitting is essentially a ritual - it should not be considered something where an inspector protects you, evaluates work, or rules on workmanship or opinions. If you have a structural engineer's report, that is the important component for any future sale.

- Rust: the "W" shape (called "I beam" by laypersons) used as a vertical brace was originally a long piece sitting with dozens of other sizes stacked outside a steel fabricator's yard for probably a long time. They are not painted. They start surface rusting when immediately exposed, which does not affect the integrity of the member. A company requests a number of beams at a certain size and shape, and the fabricator grabs some from the yard, cuts them to order, and delivers them.

- Epoxy: Can't zoom in enough, but that looks like cellulose insulation that fell from above and landed on top of the electrical box. If so, blow or wipe it off. Epoxy is an ooze.

- Handprints: Assuming referring to the outside patch, I would also assume it was cold when installed, which made the product hard to work with, and the installer pressed it into a crack/void/dimple with fingers for whatever the patch was concerning.

- Cracks: old concrete and new patches over those cracks will continue cracking. It is usually not a concern structurally unless there is movement.

- Gaping openings: There shouldn't have been a need to create openings to do the braces or crack fillers, so more info would be needed. But you should not see sunlight coming through the exterior wall.

- Sill plate: Also should not be part of work with braces or crack filling. It would be very difficult for a sill plate to break unless the entire house collapsed inward on itself. Wood can naturally get cracks and checks, so more info would be needed.

- Chunks of tubing: If PVC piping was done for the sump pump, there may be some pieces that were cut off and left on the ground. A typical jobsite has lots of pieces of things laying around that someone needs to clean up, and usually it is never the tradesperson that made the mess.

If a licensed structural engineer stated the work was acceptable, then you would be throwing money away carrying this on. The engineer is concerned with meeting the project scope, which does not include fine workmanship for these kind of repairs. Hired tradespersons just don't have the same level of care for things you own that they do not. The only way to care for workmanship is to do things yourself.