The bytes problem
First of all, you're misusing the serial.readline function: it returns a bytes object, and you act like it was a str object, by doing out += ser.readline(): a TypeError will be raised. Instead, you must write out += str(ser.readline(), 'utf-8'), which first converts the bytes into a str.
How to check when the transmission is ended ?
Now, the problem lays in the out != '/>' condition: I think you want to test if the message sent by the device is finished, and this message ends with '/<'. But, in the while loop, you do out += [...], so in the end of the message, out is like '<here the message>/>', which is totally different from '/>'. However, you're lucky: there is the str.endswith function! So, you must replace while out != '\>' by while not out.endswith('\>'.
WWhatWhat'sWhat's theWhat's the f*** ?
Also, in your loop, you write the whole message, if it's not already ended, in each turn. This will give you, in output.log, something like <<me<mess<messag<messag<message>/>. Instead, I think you want to print only the received characters. This can be achieved using a temporary variable.
Another issue
And, you're using the serial.readline function: accordingly to the docstrings,
The line terminator is always b'\n'
It's not compatible with you're code: you want your out to finish with "\>", instead, you must use only serial.read, which returns all the received characters.
Haaaa... the end ! \o/
Finally, your while loop will look as follows:
# Check if the message is already finished
while not out.endswith('/>'):
# Save the last received characters
# A `bytes` object is encoded in 'utf-8'
received_chars = str(ser.read(), 'utf-8')
# Add them to `out`
out += received_chars
# Log them
fw.write(received_chars)
# Print them, without ending with a new line, more "user-friendly"
print(received_chars, end='')
# Finally, print a new line for clarity
print()