tl;dr: forget tantalum, update your regulator to a better one.
Diodes makes the AP63205 with a 1.1MHz switching frequency in a smaller (SOT23-6) package. You can use it with ceramic caps. Linky: https://www.digikey.com/en/products/detail/diodes-incorporated/ap63205wu-7/9858424
The benefits of using a faster switching frequency are less ripple (less capacitance needed) and lower value inductor (less I^R losses). Both serve to improve efficiency and footprint. And yes, efficiency is actually improved despite some increased parasitic loss due to the higher switching rate.
Your 5V regulator can use a couple of ceramic 22uF caps and 4.7uH inductor - resulting in a much, much smaller design than you could achieve with a 150kHz switcher.
As far as tantalum caps, besides their physical and electrical issues, there’s another reason to not use them: tantalum is a conflict mineral.
POSCAPs are a good option if you really need a large value in a small volume, which you don’t if you upgrade your switcher.
Finally, if you’re really hurting for space, MPS, TI and others make regulators with integrated inductors.