9V battery (farad capacitor)

My multimeter isn't used often, only once or twice a year for about 20 minutes each time.
Every time I use it, the battery is dead.
I tried buying 9V rechargeable batteries, but they were damaged by over-discharge due to forgetting to charge them regularly.
So, I considered using a supercapacitor to temporarily charge it for 2 minutes, as supercapacitors are not susceptible to over-discharge.
The usage time isn't a major concern; enough to complete the signal measurement is sufficient, and if necessary, I can use it with the charger.
 
I purchased the casing and supercapacitor from Taobao, choosing 6.3*23mm capacitors.
The purchase links are as follows:
https://item.taobao.com/item.htm?id=807844324726&skuId=5487991620639
https://s.click.taobao.com/2lcWrWt
 
Other components can be purchased from the BOM.
Because the casing is tall enough, the supercapacitor can be angled up to 70° and float above the PCB.
 
Design Notes:
Since farad capacitors are not particularly delicate during charging, a charging IC was not used. Instead, a PTC fuse and a resistor were used to limit the current, connecting the capacitor directly to it.
The capacitor needs to be protected against overvoltage. Due to the presence of the current-limiting resistor, and considering the relatively small charging current, a 2.7V Zener diode was used for voltage balancing.
Because a charging IC was not used, the power indicator was omitted, which is slightly inconvenient. It generally takes about one minute to fully charge, which is barely sufficient.
 
The boost converter section used the MT3540 from Xi'an Aerospace Minxin, solely because its datasheet indicates a low Iq in PFM mode, at a maximum of -60μA.
A lower Iq enhances the multimeter's battery life.
However, the chip may not actually operate in PFM mode, or other chips may have an even lower Iq in PFM mode (though they may not have specified this parameter).
The MT3540 may not be the optimal solution, and feedback from users is welcome.
 
Why use a PTC + resistor combination for the charging circuit?
1. A PTC + fast recovery diode combination was considered previously, but the fully charged voltage was around 4.2V, resulting in a loss of capacitor capacity.
2. The peak current is around 2.5A. Using a computer's USB port may trigger port protection due to inrush current.
3. Considering all factors, a PTC + 5-ohm resistor combination was chosen for the charging circuit to limit the current to below 1A (a 10Ω resistor could be used for safety).
4. The disadvantage of this approach is that even after the power supply is removed, the voltage of the supercapacitor can still be seen at the Type-C port, resulting in the loss of input reverse current protection.
 
Layout Considerations:
The SW network is a moving point and needs to be as small as possible.
The remaining networks can be routed smoothly; there are no major difficulties.
Use thicker and larger traces and vias, and larger solder rings, respecting the power board specifications of the PCB.