As for chemistry and glass foam, the voltage of a cell is determined by the electronegativity of the reaction in the battery. With lithium, it can never be very much above 5 V- atoms just don't pull on each other that hard. This already uses lithium, and the chemistry won't be able to improve much bast 2.5 V.
For any given chemistry, you can't increase the voltage without putting cells in series, because the atoms decide the voltage. Any tweaks to construction, electrolyte etc. can only increase the current, by giving it more places to flow.
Please, it's as simple as a three-component boost converter - one IC and two resistors. Same thing I use to bump 1.2V up to 3.6Vto run LEDs. It takes zero space (7x7mm total.)
That's 4 mm x 4 mm (more with passives, but not too bad), and hits a solid 95% efficiency at the normal load of an iphone, and is above 90% all peak loads. Heat dissipation will be fine, all parts cost about $1.20. Low EMI.
However, its still a dozen new components. It's a ~10% tradeoff somewhere and while that may be totally worth it, its not simple. Phones do not have square millimeters to spare.
Actually, they do, when you're replacing the battery with one with 3 times the energy density. Use some of the saved space for your DC-DC converter.
Also, its not even at the stage of a hypothetical question yet. This battery would last about two weeks in an iphone under these load conditions. The only reason it "looks" possible is if you're considering a battery that is not this one.
We use resistors as inductors. Plenty of wound resistors in teeny-tiny packages exist, that's how we have metal detectors with credit card-sized boards, the literal bulk of the unit is the frame and coil assembly and board housing + adjustment controls.
Older gas charge pumps can handle it, but they're bulky and they are lossy and generate a lot of heat.
Remember that '3.7V' nominal cells range from 4.2V down to a low voltage cutoff about 2.8V (and in practice will not be let too close to that DoD). So stacking two of these '2.5V' cells will probably give a 6-4V usable range.
Remember also that the electronics is in three groups: 1.8V (most of the processor), 3.3V (peripherals), and raw battery voltage (RF front end output power amplifier). The former two will already be driven by switchmode regulators and the latter is much more flexible.
Really small devices do not have space for those, so ear buds may not be able to use this battery. But your phone, or watch, certainly can.