I’m no pro but am dealing with results of slacker roofers/“project manager” who just wanted to get the job done as fast as possible - and it’s crazy because it would have only taken a little longer to do it right.
Could be layers are starter strip with two layers (exposed and covered part of shingle). I think should have 1/2" to 1" of overlap, but many do 1/2" on rakes with drip edge. I like to see 1" overlap because with thicker architectural shingles, they won’t “droop” down to form a drainoff slope after they heat up (my Durations didn’t).
I can’t tell, but is there any overlap at this rake edge? Could be none and they tried to seal it to stop water from wicking in.
$45K sounds high but it looks like you might have a steep roof and with 5K sf may have a lot of valleys, gables etc… along with cost of tearing off the old roof.