I would like to address one of the OP's questions about heat transfer directly because the existing answers did not (yet):
[OP:] I think that heat is lost by the system since the surrounding(water)'s temperature increased, and work has been done to the system. However, when I consider the thermal equilibrium, the system's temperature must be 28 ∘C as well. In this case, is heat added to the system or not?
The short answer is: no heat is added to the system; the system gives off heat.
Heat is a transfer of energy from one place to another. So you can't "add heat" somewhere without "losing heat" somewhere else. In a heat transfer across a boundary, $q$ is positive for one side of the boundary and negative (but of equal magnitude) for the other.
The surrounding (in this case the water bath) is often chosen to be "boring" (no chemical reactions, for sure), while the system can have all kinds of stuff going on (a spark, a chemical reaction, large fluctuations in temperature). This way, you can measure the heat transfer via temperature changes in the water bath.
In the case at hand, both system and surrounding show an increase in temperature after things have calmed down. That tells us that some other form of energy (potential energy or specifically "chemical" energy in this case) has been transformed into thermal energy. This took place in the system (the surrounding is too "boring" for that).
To get back to the question I wanted to address:
... is heat added to the system or not?
The thermal energy of the system increases because of the exothermic chemical reaction. Some of that thermal energy is lost to the surrounding through heat transfer, warming up the surrounding. You could imaging that the temperature of the system first went up a lot (if the reaction is rapid), and then cooled down to 28 $^\circ$C, heating up the surrounding from 25$^\circ$C to 28 $^\circ$C. Or you could skip the details and just compare the initial and final state and not worry what happened in between, in the spirit of thermodynamics. The conclusion is that heat is transferred from the system to the surrounding. Nevertheless, the temperature of the system increased because of the exothermic reaction, which generated more thermal energy than the system gave off. In other words, no heat is added to the system; the system gives off heat.
In this explanation, I have set aside the work done on the system. The OP is vague about whether the process runs at constant pressure or not, and we don't know the magnitude of the work compared to the heat transfer; for my answer, you should assume that the magnitude of the work is negligible compared to that of the heat transfer, otherwise some of the statements might become inaccurate (such as "the exothermic reaction, which generated more thermal energy than the system gave off").