Dual battery

Remember that Lifepo4 or other lithium batteries will not like to be placed in the engine compartment as they are not chargeable at very low temps and do not cope well with high temp.

Now that they are so much cheaper than before and especially considering weight and size and amp pr cost and we all have small sized cars.
As you will be able to use at least 80% of the rated amps instead of 40% of an AGM you can either get twice the amps you need or even better half the size and much lower weight.
All over the youtube everybody is putting insane amounts of amps of lithium in their overlanding vehicles. but if you are doing a bit of math and do your cooking on a gas burner or a fire, you can manage with a much smaller battery. My 50Ah lifepo4 can run the fridge for days if it is out of the sun. Most days I have the fridge hooked up to the starter battery. 
I wouldnt take an air fryer or a microwave because of size anyways so I wouldn't waste space for an inverter.
I have a 300W very small inverter but I cannot find any use for 230V so havent put it in the car.

If I was doing the battery again, I would consider lithium, but the setup works well for me as it is so won't be changing anytime soon. I run an inverter, but usually for the kettle if I have something on the gas burner. If starting from scratch, I would look to use a dc-dc charger and the battery you mentioned.