This code does what you ask for: it counts the number of "eligible" dates filled for each ID, where the eligible date range starts at the first PRES_DT and ends 114 days after FIRST_PRES_DT. It accommodates gaps is supply and overlaps. It assumes data are sorted by PRES_DT within ID.
data have;
input ID First_Pres_Dt :date9. Pres_Dt :date9. DAYS_SUPP;
format First_Pres_Dt date9. Pres_Dt date9. ;
datalines;
1 10OCT2022 10OCT2022 30
1 10OCT2022 26OCT2022 30
1 10OCT2022 30DEC2022 30
1 10OCT2022 01FEB2023 30
1 10OCT2022 11APR2023 30
2 11AUG2022 11AUG2022 30
2 11AUG2022 12SEP2022 30
2 11AUG2022 19DEC2022 30
2 11AUG2022 22JAN2022 30
3 17AUG2022 17AUG2022 30
3 17AUG2022 14SEP2022 60
3 17AUG2022 11DEC2022 15
4 04OCT2022 04OCT2022 15
4 04OCT2022 01NOV2022 30
4 04OCT2022 15NOV2022 30
4 04OCT2022 21JAN2023 30
run;
data want (keep=id first_pres_dt end_of_eligible_dates eligible_days_filled total_days_supply);
do until (last.id);
set have;
by id ;
format end_of_eligible_dates supply_start supply_end date9.;
if first.id then do;
supply_end = pres_dt-1;
eligible_days_filled=0;
total_days_supply=0;
end;
end_of_eligible_dates=intnx('day',first_pres_dt,114);
total_days_supply+days_supp;
supply_start = max(supply_end+1,pres_dt);
if supply_start <= end_of_eligible_dates then eligible_days_filled = eligible_days_filled + min(days_supp,end_of_eligible_dates+1-supply_start);
supply_end=supply_end+days_supp;
end;
run;
