What is the 4V 800mA load? A motor/mech has inrush current that can trip the foldback and things won't start up. This is what I would worry about.
It's coming from 5Vmp solar to a TI BQ25176J LiFePo4 battery charger, which doesn't have sufficient thermal properties to handle any higher voltages without going over the junction temperature. Thought I would bring down the voltage first before powering that chip.
However, the BQ25176J is connected to both a 3.2V 20Ah LiFePo4 cell and the load, which can include a 3V 25mm motor with a stall current up to 1A. The BQ25176J datasheet says it is safe to connect directly to the load as long as the charge can complete within the safety timeout, and it certainly can. The motor is only powered for a few seconds per day.
Along with the heat - are you using the HSOP-8 package? It's only capable of 1W on a 4-layer (2oz outer, 1oz inner) 4-via 2000mm2 which is big.
I was going to use the TO-252-5S(A) variant. There is no board sketch in the datasheet that matches but it'll be like Board E with four vias and a large copper pad but on a two layer PCB. Since no thermal properties were listed I estimated a conservative 40°C/W in thermal calculations. Ambient can go as high as 49°C (in desert conditions) plus 6°C of solar gain on the enclosure, so I estimate 55°C ambient, (800mA x 1V x 40°C/W) + 55°C = 87°C which is well below the recommended high temperature--and that's under the worst possible conditions.
MLCC 1uF cap is never 1uF in practice. Lucky to achieve 1/2 that when you look at the mfgr graphs and include aging. Even 10uF would not be a problem here assuming the load is not demanding 800mA+ on startup.
I can do some 10uF, should not be a problem.
Would you use even more capacitors for that load including the motor startup current? I'm not terribly constrained by space so I can put bigger things on the board. It'll (probably) use a TI DRV8411A motor driver, which recommends a 10uF for bulk capacitance, but given your comments about aging I may go with like 100uF or something.