Could I use this for a rp4?

In theory, yes, but you will need to use cables to connect them with RUN, PEN pins

  I am looking to use super capacitors to provide enough power to the pi so it can shutdown safely.  If this board would work for that, do you have super caps available that would work with this board?

Yes, but only the 4000F @ 4V2 V connected to the battery socket.

If super caps won't work, could I supply power with 4 (or more) AA alkaline batteries as the power necessary for a safe shutdown?

Try, it should work, use 3 batteries, so the  voltage will be 4 x 1V2 = 4V8. It is too high, so please use them discharged, and charger will keep them undercharged, probably. Logically should be working.

I am having trouble finding the pinout for the HV3, how do I run cables from the rpi4 to the run and pen pins of the HV3? I am guessing since you mentioned that, I can't just put the HV3 on top of the 4 with the gpio connector on top of the gpio pins of the rpi4.

Can a diagram be provided on how to connect the run and pen pins on the UPS and where they go on the rpi4?

After I connect the run and pen correctly, I just need the 4000F @ 4v2 v with the proper (JST XHP-2?) connection to plug in. Do the scripts that detect power off then shutdown and power on need any modification?

Also, I have read up on lifepo4 batteries, and they seem to able to do what I need, stay in vehicle without danger of exploding or off gassing, and the HV3 can accept them.
Could I just buy this battery

https://pimodules.com/product/pico-lifepo4-battery-4000-mah-2c-with-mounting-plastic-base, plug it in the HV3, connect the HV3 properly, and be good?
Alternatively, could I buy this board,

https://pimodules.com/product/pico-single-lp-lf-li-ion-18650-battery-holder, connect it to the HV3, get a lifepo4 battery and be good?