Problem SOLVED!
I will describe the course of action, should anyone encounter a similar incident in the future and come across this thread.
I assumed that the wrong value in the ‘rain’ column is given in inches:
4.984 inches = 126.6 mm
I know from the PWS panel records that 15.0 mm of rain fell that day:
15 mm = 0.590551181102 inch
I subtracted the false value of 4.984 from the total value of 5.294 from the ‘rain’ column for the entire day:
5.294 - 4.984 = 0.31 inches
Now I convert this difference into millimeters:
0.31 inch = 7.874 mm
From the known precipitation value of the whole day (15 mm) I subtract the precipitation value from all observations (records) except one false one:
15 mm - 7.784 mm = 7.126 mm
The result of the above subtraction to the true (or close to true) rainfall value, which falsified the daily results. I convert it to inches:
7.126 mm = 0.280551181102 inch
I substitute the latter value in the database in the appropriate row and column:
echo “UPDATE archive SET rain=0.280551181102 WHERE dateTime = 1746259200;” | sqlite3 /var/lib/weewx/weewx.sdb
(I didn't back up the database because I run all the time on a local copy of the database on my laptop, not on a Raspberry Pi that supports PWS).
Now rebuilding the daily statistics:
weectl database rebuild-daily --date=2025-05-03
And everything looks as it should :)
Thank you for your help and hints - although they did not solve the problem by themselves, they guided me to the right solution.