Okay I have to ask.
When you read the ACS, what did you think was going to happen on the checkride when you read section V.A “Intercepting and Tracking Navigational Systems and Arcs”, knowing your instructor hadn’t covered it?
https://www.faa.gov/training_testing/testing/acs/media/instrument_rating_acs.pdf
How about when reading the Instrument Flying Handbook, Chapter 9?
How did you prep for the written? Reading the FAA pubs, or a ‘cram but don’t understand it’ app like Sheppard? Did your instructor review the topics in the written (required) using a written checklist (sadly not required)? Did they ask if you had any questions about what’s in the FAA pubs?
I assume they only flew with you for the required 15 hours. What approaches and activities were you doing during the other 25 for the rating?
Before you took the ride had you ever heard the colloquial phrase “if it’s in the panel, you have to know how to use it completely”?
I only ask as a warning to others, but you do have to know what’s in the ACS, FAR/AIM, and FAA pubs like the Instrument Flying Handbook, and know that you can perform it all, if the aircraft is capable... even if the instructor is a ninny and somehow missed teaching it.
It’s surprising to hear PIC screwed up that badly. Their syllabus used to cover all of this. Was the instructor using their official syllabus? If not, you need to have a chat with them about a refund, I think. At least one person here in the past was an instructor for them.