There are practical applications of S/GR ....
A major one being the operation of certain flavours of GPS systems and the interaction between Earth orbiting clocks and Earth surface based clocks.
A.
Clocks on Earth run slow, compared to high geo.sync orbiting satelite, by some 45 microseconds due to GR (ie earth clock closer to the centre of the nearest large gravitational mass (centre of the Earth).
B.
Clocks in high geo-orbit run slow, compared to earth surface clocks, by some 5 microsends due to SR (ie the geo-sync-sat is moving fast relative to the 0 speed surface clock).
C.
Combining the two "slow downs" it is clear that the geo-sync-sat clock appears to run some 40 ms fast, equating to an accumulating GPS inaccuracy of some 5 miles per day.
Without knowledge of relativity (space/time) GPS would prove worthless within an hour, or a month, or a year (depending upon application).
There are other applications too, but GPS is interesting since it applies both GR and SR effects.