Delayed RESET to MCU pin
The primary concerns for this design are the choice of both Caps and how that affects Boot reset time, Brownout time (BO) with solar input and load current and thus stability of reset threshold and mAh of capacity with a leaky ultracap. It is unknown if the application is intended to run overnight and what the brownout duration of solar input is expected.
The leakage resistance of the tantalum cap of 100uF 4V = 1MOhm thus the voltage may be attenuated with series R of 1M by up to 50%.  Although the POR threshold is programmable, the leakage R has a variable tolerance. The POR has a filter but unknown if it has hysteresis, so noise might be amplified at the threshold so this cap choice would be poor due to leakage and Rs=1M. A much smaller cap will have a lower leakage current that ought to be used.
Since the supercap charge time constant is much greater than the RESET time constant of 100s, it becomes irrelevant for time delay. You could use 1ms instead
Thus only the threshold for detecting RESET ON and OFF and hysteresis are relevant.  Consider 1.75 to 2V

Other comments.
The size of the Supercap depends on the ratio of min uAh charge available and uAh load expected without brownout duration based on historical residual charge voltage and regional solarity.
The power consumption for low f clock rates may be considered low (1mA) if peripherals are managed so a large Reset capacitor is not necessary with a 100s LPF and ripple reduction from a DC source.  Consider dV/dt = Ic/C for both charge time and leakage decay time affects both time to Boot ( Clear reset) and Brownout time (decay to Reset)
The supercap may have a high ESR (100 Ohms)  It may also have a low voltage rating.
Consider both the mAh of charge time needed to boot and mAh discharge time of the application before brownout and the ESR of the supercap for stable reset threshold detection.
Hypothetical analysis

Consider uC low voltage threshold of 1.75V and use 2V for some margin before reset is removed.

Consider sunrise current of 10% of rated or 590 uA and a 15 minute boot time from 0V which is ~ 150 uAh charge rate.

Consider a total daily charge capacity of 8h at 25% or 5.9mA/4 * 8h = 11.8 mAh

what capacity is available from 3V to 2V for a 16h dark time from 2.9V (LED Vf) to 1.75V the uC Vdd min rating?

11.8mAh /16h = 737 uA average

25% might be too much if cloudy days are expected to sustain the operation.

what is the maximum and average climate temperature&gt; This will reduce a 10yr lifespan by 50% for every 10'C rise above 25'C.


C= Ic * dt/dV = 590 uA * 15 * 60s /2V = 0.265 F
Choose 300 mF, for longer backup time or uAh, consider 1F.

only consider those with known leakage current ratings if holdup time is critical which also depends on temp.