AltSoftSerial does not work on Teensy 4.1. The main reason is a belief that 8 serial ports are enough for anyone (kinda like 640K on old PCs....) Likewise, SoftwareSerial when used with non-serial pins has limited support for transmitting, but not receiving. Since there are 8 real serial ports, pretty much no work has gone into SoftwareSerial support on Teensy 4.1.
Kurt's FlexIO serial library is probably your best path to a 9th serial port on Teensy 4.1.
I really can't help much with Arduino Nano. I don't have that board. I can tell you I did test AltSoftSerial on Arduino Uno, which is supposed to be essentially the same hardware. AltSoftSerial absolutely does work on the 2 genuine Arduino Uno boards I have (R3 and the original 1st release).
If your Arduino Nano is actually a cheap Chinese counterfeit, consider the chip is probably a countefeit too, not actually the real AVR chip made by Atmel/Microchip. I've been told the counterfeit AVR chips have many minor differences which don't affect simple programs. If you're seeing a program like AltSoftSerial not work as it should, try testing on known-genuine hardware with a real AVR chip from Atmel/Microchip.