Understanding transformer datasheet
Primary inductance is 2.8 H as specified - this will have been measured/proven with the secondary open circuit because if the secondary is not open circuit then it cannot be easily measured.

At 400 Hz the impedance will be \$2\pi\times 400\times 2.8\$ = 7037 ohms reactive and draw 0.85 mA from a 6V RMS applied signal.

The 600 ohm impedance is when the secondary also has a 600 ohm load.

The 150+150 you refer to is when the primary and secondary both have centre-taps. If both primary and secondary only use one half of their respective windings, the nominal impedance becomes 150 ohms - this is because impedance is proportional to turns squared on a transformer and half the turns quarters the impedance. Given the transformer is designed for telephone applications (hence BS6306 being mentioned), the full winding is designed to be optimum for a 600 ohm load and therefore 150 ohms when half windings are used.

2.8 H does seem large but if the AL of the core is 10 uH per turn then 1000 turns would produce 10 H because inductance is proportional to turns squared. Clearly, to get 2.8 H only 529 turns are needed hence 10 uH x 529\$^2\$ = 2.8 H.