Does anyone know if there are similar drive restrictions for 5.25" drives for the Amiga as there are for the 3.5"?
The restrictions for 3.5" drives are not due to the storage capacity, but due to the electrical interface between the host system and the Amiga. As the electrical interface is identical, it is quite certain that you run into similar problems with 5 1/4" drives than with 3 1/2" drives - with one difference: 5 1/4" drives typically do not implement the diskchange signal anyhow.
i.e. Did Commodore attempt to shove more bytes on the floppies than anybody else did?
Yes, but this does not require particular drives. The reason why this is possible is simply that the inter-sector gap of the Amiga format is shorter than that of the PC, and the reason for that is that the Amiga always reads and writes entire tracks, whereas the floppy disk controller of the PC only operates on entire sectors. For that, it requires a longer gap between sectors to compensate for mechanical inaccuracies. The Amiga does not need this.
Or can we use C64 drives and or PC drives without (many) issues?
You will (most likely) run into the very same issues than with 3 1/2" drives, but not due to the storage capacity, but because CBMs floppy bus, which is almost, but not quite identical to what a PC uses. Many drives of the same age could be jumpered to support other interfaces, but the modern (ehem) floppy drives are so cheap, they are just "PC only" because that is the only feature that is needed on the market. If it is needed at all - floppies are obsolete since years, so there is not much demand.