Does CURRENT_STRENGTH_NEW limit current?

Hi,
current strength specification has nothing to do with limiting output current to a certain value. The mA value defines the maximum load current that keeps output voltage drop within the logic level specification of a certain IO standard. Maximal output current, e.g. into shorted output is much higher and exceeds in most cases FPGA maximum rating so that the output driver may be damaged.

See for example the output characteristic of Cyclone 10 LP CMOS 3V IO standard with 4 mA current strength according to IBIS files.

The only IO standard that limits output current to a safe value is LVDS 2.5 V. HSMC breakout adapter is obviously designed to use this standard.