Is delaying a flight by a short time (several minutes) a "reasonable measure" under EC261?
I highly doubt it. Airline schedules are complicated with lots and lots of dependencies, so they can always claim that a delay to save one connection will jeopardize other connections.
The regulations (see full text at https://eur-lex.europa.eu/legal-content/EN/TXT/HTML/?uri=CELEX%3A32004R0261) don't specify what "reasonable" entails, so that would have to be decided in court on a case by case basis.
No one can predict what a judge might consider "reasonable" in your specific case but "a few minutes" is not precise enough to guess.
The decision to wait (or not) is done by the operational staff of the airline taking a lot of current data into account. Since you don't have access to this data, it would be quite difficult to prove that the decision was "unreasonable".
EDIT after delay details were added
The delayed flight arrived at 19:45 while the connecting flight departed at 20:00.
That would probably be a no go in court. Scheduled arrival and departure are typically defined as "set and release of the parking brakes of the aircraft" (which is easy to record automatically).
If you want to make a connection, there are whole lot of things that need to happen between these two points in time.
- The deplaning mechanisms needs to be connected (jet bridge or stairs) and doors need to be opened
- You need to deplane
- If required, you have to hop on a bus, wait until its full and then ride to the terminal
- Enter terminal,
- Potentially clear security, immigration and/or doc checks somewhere along the way.
- Potentially transfer to a different terminal
- Potentially make a bathroom stop
- Hike to your departure gate. There may be a doc check along the way as well.
- Arrive at the gate before the "gate closing time" which is typically 15 minutes (or a little more) before the "scheduled departure time".
- If you have any checked luggage, that also will need to be unloaded, routed, X-rayed (maybe), transferred to your connecting plane and loaded.
All of this adds up and depends a lot on your specific connection, the airline, and airport layout. Hence the airlines define "minimum connection times" (MCT) for different connection types and will only sell tickets that have at least that amount time between scheduled arrival and departure.
The shortest MCT I'm aware off is Vienna airport with 25 minutes for a Schengen to Schengen connection, but that's an outlier and most MCTs for "normal connections" are in the 45min-60min range. Some can be substantially higher (for example US international to domestic connections where have to clear immigration, customs and security on arrival).
Unfortunately, MCTs are not well documented or published, so you would have to do some digging for your specific case. Assuming an MCT of 45 minutes (which is on the low side) and a difference between arrival and departure of 15:00 minutes, the airline would have to delay the plane by at least 30 minutes to give you a reasonable chance of making it.
Personally, I would not consider that "reasonable" since it's likely jeopardizing downstream connections and other flights. Aircraft these days are often scheduled to fly back to back to back, so there is little slack to absorb even smallish delay.
Some airlines are more hard-nosed than others. Personal anecdote: My inbound was delayed so I had an extremely short connection with the gates being far apart (Denver). However, I got off the plane quickly, I know the airport and I can run fast, so I made it to the departure gate with 2 minutes to spare. I then scan my boarding pass and it beeps red. The gate agent looked at and it said "Sorry Mr. XXX, we didn't think you would make it so we have given your seat away already".