What would happen then with the output of the charger? Because we have
now the situation of two "DC-sources" which are connected parallel and
have different voltage. Or am I wrong?
You are wrong. By definition, the voltage at a single point or 'node' is the same for all components connected to it, so the charger and battery will always have the same voltage when connected together.
This is why you are using a 'Constant Current, Constant Voltage' regulator rather than a straight voltage regulator. When disconnected the charger will (when properly adjusted) put out 8.4V. When the battery is connected and tries to draw more than the set current, the charger will drop its voltage to limit current. At the same time the battery voltage will rise due to the charging current. When battery voltage reaches 8.4V the charger will progressively lower the charging current to prevent the voltage from going higher than 8.4V.
The LT3741 itself is not a battery charger. You can safely use it to charge a Lithium-ion battery provided that you have mechanisms in place to handle fault conditions such as an over-discharged battery (must be charged at a lower current until reaching 3.0V/cell), charger malfunction (not limiting current or voltage), cell voltage imbalance, and excessively high battery temperature. A BMS (Battery Management System) or PCM (Protection Circuit Module) does some of that. For the rest you need extra circuitry, or manual monitoring and intervention (not recommended).