Not trying to keep it a secret, just don't know how to answer a relevant question that hasn't been asked.
Since you have asked...
The first phase of the project involves a periodic predefined motion of a mini servo. I plan on the ESP going to sleep for 30-60s between cycles. An optional switch closure will be used to trigger a LED and piezo buzzer.
The second phase of the project involves connecting to the ESP via bluetooth to define the servo motion patterns as well as other control of the unit and possibly notifications based on battery level and the optional switch closure.
The servo I am using is capable of being powered by either 3.3v or 4.5v source voltage. It also can handle the 3.3v signal from the ESP.
Ah some details at last, would it have been so difficult to put them in the original post ?
If by 'efficiently' you mean longest battery life, then you do need to work through the numbers, do not assume an obvious solution is the best.
For a project that runs continuously, with a moderate power drain, then a switched converter might indeed lead to longer battery life, you can then drain the batteries below 1V.
However if the project will be put periodically into sleep mode, and an ESP32 can go down to 8uA, then a switched converter may not be a good choice. The switched converter will have a quiescent current, so even with the ESP32 at 8uA, the switched converter might draw 2-5mA. This will obviously drain the battery. In these circumstances a good low drop out regulator could give a longer battery life, even if the batteries are then only drained down to 1.1V each.
Now if you could find a switched up\down converter with a quiescent current of a few uA, then it would be a good, almost universal solution, but otherwise its a case of doing the numbers, taking measuremtns of run current, run periods, sleep current and sleep periods, and only you can do that.