Nobody wants to be on record as having said that but I'll bet a bunch of us thought that...

:D

Code is different from country to country, state to state, but the big one is year to year.
The relevant code would be the year the panel was installed or updated.

^^^This for sure. Half the stuff we do is done after the inspector walks away.

your interpretation of clearance is correct.
closets are a no go for panel placement.
your panel is low, which is a good thing. the switch is set at 48" above finished floor. the top breaker, not the top of the panel, can't be higher than 48" aff
the question i would ask is what is on the other side of that wall. why not rotate the panel to face the other side of the wall.
the communication panel can stay where it is.

The family room is on the other side.

We are going to start the shelf an inch away from the panel towards the washer and dryer. The 30" will start at the panel and go towards the door.

I'll clear a few things up as a ICC Master Code Professional . If this is a ground floor apartment unit it is required by current code to have the disconnect at 48" rather than 6'7" so the owner occupant,if accessible, can disconnect. (I'm not horribly keen on the requirement but it is what the code says)
Regarding the shelving : I'd eliminate the small section in the pic and place melamine shelving (not able to hang cloths) anywhere you'd like other than the 30" clearance in front of the panel. I measure that 30 as on center line of the equipment. Sorry to say that shelving could not go in the area above the panel even if it is low for ADA. Nothing foreign above or below.
If the owner wants something installed after final I wouldn't do it. People are stupid/designs are stupid at times/and litigious at every single turn. The panel and com panel should be in a laundry area design wise IMHO with shelving over the washer dryer on the opposing wall of the entry to the room.

I did this once, but I made darned sure that nothing could ever be placed or hung in front of the panel. There is the letter of the law, and the intent. You want to make sure that the intent is met, for everyone's well being.

The inspector said if I hung the shelf above the panel, it would meet code. After that, he wouldn’t know if someone hung their coats off it, blocking the panel. Of course the coats are easy to remove.

The inspector said if I hung the shelf above the panel, it would meet code? No No and No but not my call/my jurisdiction. Working space clearances go to 6'6"
The whole concept of no hanging is a pet peeve of mine, the panel overheats and possibly sparks right by a whole lot of cotton fire load. The apartment building catches fire and multiple families are on the street and someone's kid has died.
That concept is something you'll never see me on TV trying to explain, nobody dies on my watch regularly comes out of my mouth. Also "no Station Nightclub" on my watch....