I'm swapping a fresh set of heads on the 5.7 Hemi in our 2004 Durango and other than being a pain to get at most everything it's getting there.

Of course something has to break, the ignition noise capacitor on the back of the left cylinder head broke when I was taking the bolt out.

It's a part number 05149011aa which is of course no longer available and doesn't seem to have any superseding number for a replacement.

Is it going to really make a difference in how the radio sounds if it isn't there?

On the AM band yes makes a hearable difference, on FM probably no.

Does the opposite side cylinder head rear have a corresponding capacitor you could measure,
or does the FSM or parts list have the micro or milli Farad value?

A car stereo shop could look at it, measure, and guide you to an aftermarket alternative,
or a “Ham Radio” friend.

Chrysler vehicles used to be very very good from the factory at suppressing the “pops” and buzz noises on the AM band.
My 1995 truck was still good
but my mother’s 2005 extended Town & Country minivan is horrible and it is not a fault inside the factory radio.

On new conventional and EV vehicles Toyota and Mitsubishi still do the skilled engineering work needed
but most others want to skip, such as Tesla.

What broke, the actual cap/wiring, or just the mounting tab?
Zip ties will fix a tab issue, but I agree you probably won't notice a difference without it.
Easy enough to try without, can always add later.

There’s only one, on the back of the drivers side cylinder head.

The metal attaching tab broke off.
Since it’s what grounds it to the cylinder head and mounts it, it’s trash now.

Once the intake is installed, there’s no way to reach that area to install one.
The engine sits so far back under the cowl.

The lettering on the plug strongly hints that inside the plastic there is a

0.47 MF capacitor rated 250 volts.
Very common.

I would suspect that badly designed plug vibrated up and down
and over time a fatigue crack worked its way across the copper/cadmium plated mounting tab.
Tab could be plated steel.

Since the part is no longer available I would try to solder a wire a few feet long to what is left of the tab in the plastic plug and then ground the other end of the wire to a vehicle ground off the engine that is easy to see and inspect, and where vibration is much less.

The other bank of the engine should also have a capacitor that does the same RFI job but looks and is mounted differently.

In addition to reducing radio interference, the capacitor also reduces the “spike voltage” on the ignition coils
so in the worse case the way more expensive coil(s) might fail in the future.

Or if the plug is still available, buy a capacitor and attach one lead to the plug and the other lead to a soldered or crimped ring terminal.

I would bet that a lot of those have factory RFI reducing and coil voltage spike limiting parts are now cracked.

Extended the harness while you have access.
Then you can plug in it and bolt it to firewall if needed later.