(I'm taking for granted that your visa will still be valid for this visit)
This is quite the opposite of a "visa run".
A visa run is when you briefly exit and the re-enter a country, to "reset the clock" and stay longer.
For instance, say country X gives you 30-day visa-free entry (or you are allowed to stay 30 days max each time you visit with a visa). A visa run is when:
- You enter country X. You are granted the right to stay for 30 days.
- Shortly before the end of the 30 days, you travel to country Y
- You stay in Y a few days or even a few hours
- You come back to X, and you get another 30 days (or at least you hope to).
- So other than a few days/hours, you effectively stayed 60 days in a row rather than 30.
- Rinse and repeat.
You are doing the opposite: you are entering and then re-exiting Singapore for a few hours. This happens all the time. While it may have gone down quite a bit with the advent of video-conferencing, people visiting a country for a few hours for a meeting is still a very common situation. I bet early and late flights between KL and Singapore have lots of people on board doing exactly that (back and forth on the same day).
And of course there are people transiting, and that's a a lot more.
Sure, they would prefer for you to stay longer and spend more money in Singapore, but from an immigration point of view, there's no issue at all here.
Granted, your itinerary may seem weird, but they've seen a lot worse, and you have a good explanation for it.
It's even possible you may not even go through immigration in Singapore. Since your India-Singapore and Singapore-Europe flights will probably be booked separately, you still need to have the right paperwork to enter Singapore (your valid multiple-entry visa), but if you don't have checked bags you don't need to, you can just stay a few hours/days in the transit area and they take your next flight. If you have checked bags and you can't get them checked through, then you will go through immigration (in and then back out a few hours later), but again, no issue there, it's so common they won't even blink.
As this is effectively a self-transfer, remember to consider the risks associated with a self-transfer when selecting your flights. Have plenty of buffer. I would personally probably book a night in a hotel downtown and spend a good evening there enjoying the fine food before flying back home, but that depends a lot on the timings.
Now I'm hungry just thinking about it :-)
