TPS61280: Help recommend the right IC, or new Device：a battery for silicon anode materials，This battery must be used with an IC with bypass function.

Part Number: TPS61280

Hi，

We are currently evaluating a new material, a battery for silicon anode materials. This battery must be used with an IC with bypass function. Otherwise, the battery voltage is too low. If the battery is ok, the battery that uses this technology will be used. Use this IC;
The voltage is 2.5-4.4V, the system needs a stable voltage higher than 3.5V, and the output current does not exceed 1A;
So we want a battery front-end boost, the battery voltage is higher than 3.5V bypass, boost the voltage below 3.5V to 3.5V;
Find the following:
TPS61256 frequency is 3.5MHz, Iq is bigger, cheaper
TPS61280 frequency is 2.4MHz, Iq-2uA, slightly more expensive
Help recommend the right IC, or new Device;

Thanks a lot.

Elsa Duan