Regarding why Rebbe Rayatz did not establish 3 Tammuz as a holiday, unlike 12 and 13 Tammuz, it can be explained as follows: the primary role of the leader of the generation is to influence the entire generation, with personal matters being secondary in comparison. During his time in exile, Rebbe Rayatz’s ability to exert influence was greatly restricted, which is why he did not establish 3 Tammuz as a holiday.
However, the connection of Chassidim to the Rebbe should encompass everything, as the Rebbe is the collective soul and everything that happens to him is connected to all Jews. Therefore, Chassidim should also celebrate 3 Tammuz.