To answer your specific question: no. There have been and continue to be lots of CPUs that have things that could plausibly be called a “bit size” that aren’t a power of 2. Note that the “bit size” can refer to a few things (the width of the bus between the CPU and memory, the native size of a pointer, and/or the native width of the arithmetic units). I’ll give examples of each.
On essentially every “64-bit” computer, the bus to memory is not 64 bits wide. For example, the Apple M4 ARM CPUs are 64-bit but have a 128-bit memory bus over which they communicate something like 43-bit physical addresses. ARM has always been this way; the original 32-bit ARM1 had 26-bit physical addresses.
As to pointer size, the best example is probably the currently-being-developed CHERI architecture which is 64-bit arithmetic but 129-bit pointers.
For an arithmetic unit example, the floating-point unit on Intel CPUs was traditionally 80 bits wide. These days, it’s emulated on a 128-bit wide SSE unit but you still see 80 bits in code a bit.
MySQL often has moderately higher performance (particularly for workloads where you want your data clustered by PK, which is how InnoDB is natively structured) and its replication system is much more flexible than either of PostgreSQL’s. I like Percona personally, but MariaDB is fine too.