Your SDCard probably doesn't have the firmware/bootcode for a 3B+, or it's a NOOBS SDCard. If it's NOOBS forget it, write a new card with plain Raspbian Buster 2019-07-10.
If it's not NOOBS then stick the SDCard back in your RPi3B
sudo apt update, sudo apt -y dist-upgrade then sudo poweroff
Try that back in the 3B+.
If it doesn't work put it back in ...
This is a typical behavior I have seen with a "weak" SD Card. It sometimes works or not maybe depending on different hardware because of very small different electrical characteristics. You wrote that you always use the same SD Card. I suggest to try with another SD Card to exclude that's not the reason.
You could put files in the relatively small boot partition.
Otherwise NO. macOS doesn't (actually won't - it could) support ext4 partitions.
There are a number of 3rd party options for ext4 support, but each new release prevents these from working.
Transfer files over the network - there are lots of options; FTP, nfs, Samba, afp etc.
No. (Although this depends on what you mean by mutually exclusive - booting or setting OTP bit.)
You don’t say which model Pi you have; the instructions to set the OTP bit only apply to the Pi3.
The OTP bit is set by default on the Pi3B+ (as vcgencmd otp_dump | grep 17: shows) but it boots from SD Card if no device is detected within 5 seconds.