I would say this is the heater matrix/core just the fact you point out the coolant in the bottle is the same as what's in the carpet.
In any case it's a big job most of the dash (bottom half) needs to come out then fight your way into the heater box, the coolant pipes connect to the matrix in the engine bay so need to disconnect them and then pull the matrix pipe work back through the bulkhead, all in a very tight space, if you've not done it or have little experience working with cars then this is one to be left for a garage
In any case it's a big job most of the dash (bottom half) needs to come out then fight your way into the heater box, the coolant pipes connect to the matrix in the engine bay so need to disconnect them and then pull the matrix pipe work back through the bulkhead, all in a very tight space, if you've not done it or have little experience working with cars then this is one to be left for a garage