Long War of the Chosen does some changes to the Grenade Techs which means Mag and Beam Launchers don't get added to your inventory correctly.

To fix this, go to

\steamapps\workshop\content\268500\2571476425\Config\XComTemplateEditor.ini

and change these lines:

V = "PlasmaGrenade"
to
V = "ExoSuit"

V = "AdvancedGrenades"
to
V = "WARSuit"

Also, comment out the lines containing "BeamGrenadeLauncher" - Add a semicolon at the start of the line.

This will make it so Mag and Beam Launchers unlock at Exo Suit and WAR Suit research, respectively. Not quite how it works originally, but since I know ♥♥♥♥♥♥♥♥♥ about X2 modding, this is the best I could come up with.