1. Consideration - USB-C PD: Implementing USB-C I will mainly request for a 9 VDC supply. If negotiation wasn't successful only 5 V are provided.
2. Consideration - Battery: 4 NIMH cells => charging voltage: 5.2 V, delivered voltage range: 5.2 V down to 3.6 V (i.e. empty).
3. Consideration - Required system voltage: System supply voltages requirements are 6 V (P < 100 mW) and 3.3 V (P < 5 W).
What I found so far: Plenty of (hybrid) buck-boost battery management controllers (BQ2000T, ..., BQ25910) that doesn't fit the combination of boosting a 5 V USB supply for the required battery charging but also boosting later on to the required 6 V from battery (i.e. 3.6 to 5.2 V) if the USB source is absent.
I wonder if TI doens't have a battery management controller IC, that provides buck-boost from the input source as well buck-boost from the battery to provide a higher system voltage than the battery delivers?
A solution is of course a further booster circuit. But hope to find a chip that already organizes this application for me.