How can energy "physically" be fed back into the grid?
I cannot comprehend how, for example, multiple homes can feed their ... energy into a grid using the lines of the public utility.

That's the way the power stations do it, so why not? All that is required is to keep the AC frequency correct and in-phase with the grid and then raise the voltage above the grid voltage. Current will flow from the higher voltage to the lower.

Can excess PV be fed directly into the grid using an inverter?

Yes, but a grid-tie inverter is required. It will maintain frequency and sync with the grid and also have features to disconnect in a guaranteed safe manner when the mains power is lost. This avoids you trying to power up the city with your little solar panel and also avoids electrocution of the lineman out doing the repairs.

Or is it necessary to go through a &quot;middle man&quot; like a battery, and from there the DC can be converted to AC.

Theoretically no, but there may be practical or separate reasons to have one there.

Is the utility automatically distributing the excess energy from individual homes to other loads in the grid?

You can consider it like water feeding into the national pipework. It will generally be drawn off by the nearest consumer. If the grid voltage starts to rise then the load schedulers need to reduce supply.

Are they &quot;bleeding&quot; it off somewhere similar to a pressure valve in cases where they cannot handle all of it?

In the case of steam power stations, yes, the excess steam will have to be vented. Wind turbines can be turned out of the wind. Hydro can be shut down quickly. Gas turbines can shut down quickly.

Another issue is there are multiple power producers that are using lines that stretch hundreds of miles, and now you have homes feeding energy back into these lines, so I am guessing that a single power producer needs to be in charge of an entire section, so there is no congestion.

It's more likely to be controlled by the network company these days.