I am using a BAUDrate of 115200 since I cannot make a connection to my printer with the advised 250000 rate. Are there any downsides or limits I reach earlier given by the lower BAUDrate?
Baud rate is the rate at which information is transferred in a communication channel, given as a number of bits per second (bps). So a baud rate of 250000 is capable of transferring a maximum of 250000 bits per second (31250 bytes/s). When working with serial ports, both ends of the communication line will have to "talk" with the same speed - the same baud rate - to understand each other.
So when using a baud rate of 11520 you will theoretically be limited to transfer data with about half the speed of 25000. If you are transferring large amounts of data, this might be a limiting factor for your application, but if you are not pushing the limits of your serial port, it probably won't matter at all.
If your printer doesn't have an SD card then the whole communication between computer and arduino is performed "live". There is kinda buffer of data which arduino can swallow. Then it needs to process it (and then can send some reports to your app) and then arduino is ready to get new "set" of instructions to work on.
Now. If a baudrate is to low then there could be a situation when arduino finishes its job and has to wait for new bite of data. In such a situation you can see the printer pauses printing as it waits for signals from arduino as it waits for data from computer. That's more or less a downside of a low baudrate.
If you have a SD card then the data is sucked from it but reports are still send by port to show results on screen. In such situation you can see sligtly late screen update.
A screen means just a fun of live preview but breaking printing process (caused by late data send) means your hot nozzle stays over the same position which can destruct a surface or even fry up a plastic a bit. It also oozes and therefore creates lasting artifacts.
Resuming - low baudrate is evil ;)
If a GCODE line is about 30 characters (which is about the norm), you can send at most 420 of them per second at 115200 bps.
If each GCODE prints 0.15 mm (for example in arcs), you would be limited to 63 mm/s in arcs/circles (straight lines are not an issue).
If that's limiting for you, then you should find a way to set 250 kbps.
You don't mention the firmware you use, but if you use Klipper, which compresses data over the serial line, connection speed is not an issue.