Charging coin cell battery / feeding the circuit at the same time


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Hi, i'm designing my bluetooth low energy board and i need your help regarding the power management.
i use a coin cell lithuim battery LIR2450 to supply my board. this battery is a rechargeable one. here's the datasheet of the battery :

I'm using a switch to select between charging the battery and letting the battery supply the circuit board.

the charger circuit is the MCP73831T and it deliver 4.2V to charge the lithuim battery. here's the datasheet :

When the battery is fully charger the voltage is equal to 4.2V and when is completly discharged the battery voltage drop to 2.75V. this is the reason why i use a Ultra-Low Power Buck Converter, the TPS62737 , to drop the voltage to 2.5V here's the datasheet :
this buck conveter is good for my board because it has a good efficiency in low current and my board consume a low current.

and i want to know if the voltage drop of the diode won't deteriorate the power efficiency?? because i want that the battery will hold energy for a long time. if there is another solution for my problem i'll appreciate that.

note that the circuit consume in average when all the circuit are idle mode 20uA.
Only issue I can see is that the Lithium Iron cell has no protection and given they have a history of bursting into flames for no apparent reason, I'd be thinking about that.
Your overall plan looks good. The TPS datasheet should have some transient response information or plots. Another approach is to eliminate both diodes and connect the battery charger directly to the battery, which is connected directly to the TPS. This only works is the battery charger has nothing after its output rectifier other than filter capacitors. anything else will drain the battery when the USB is unplugged, requiring a diode between the charger and the battery.
I was thinking along the lines that other manufactured packs have i.e. encased monitoring with feedback to the charger or cut-out in event of over-temp or over-charge.