It has never happened that way in any 5e game I’ve run or participated.
Player will just say “I cast Heal using xx spell slot to heal Mr. X. It heal him up xxx hp.” Then he roll the dice and that’s the end of it.
There are not many special bonuses in D&D 5e, it is designed to be much more streamline, fast, with much less bookkeeping than previous editions. And if certain character have any special bonus, they are expected to remind DM or else they don’t get to use it. That is the case in any 5e game I ran, played, or observed.