Thermal bridge - recessed balcony with brick exterior wall converted into part of bedroom

[Bence]

House with brick facade and wooden frame built in 1961.
Previously recessed balcony converted to a protruding balcony (see sketch).
Previous brick outer wall now part of the inner wall (orange) forming a massive cold bridge in the room.
The new outer wall (green) is only 15 cm and appears poorly insulated.

Considering additional insulation on the new outer wall.
Would like to address the cold bridge at the same time.
-Can you make a slit, perhaps 5 cm(?), in the brick wall at the corner of the new outer wall?
-The slit could be concealed by internal additional insulation of the new outer wall.
In the slit, you could insulate with mineral wool (?)
-Can you rent a diamond cutter with a cutting depth equivalent to a brick?
-Is there a risk that vibrations during cutting could cause the outer wall to crack?