Cool that your bringing you own heat to Germany with you.
Plants at that size can appear to grow slow, but just a couple inches growth is probably doubling its mass. And it doesn't really look unhealthy.
I'd say 4-5 hours sun daily is too little light to see it grow fast. If your house is warm, it would be surprising not to see it stretch and lean with that little sun. Cooler temps with less sun is less likely to result in stretch, just slow growth. If you can, I'd supplement their light with grow bulbs and give it at least a 12 hour day, preferably a few hours more. That will usually add a little heat too, which they'd probably appreciate. Growing pepper starts in a window (no supplemental light) at your location during March and April simply won't produce the rapid growth you'll see with supplemental lighting and, living at a more northern latitude like I do, giving them a good head start pays off.
A bigger concern is probably watering every night. Again, it does look reasonably healthy and isn't showing visible signs of overwatering, but it seems unlikely it would need that much and overwatering can definitely stunt peppers and lead to bigger problems with the roots. If your media mix is heavy (adding compost will make it heavier), that can slow growth and also increase the harm from overwatering.
NECM brings up soil versus mix, which is an important point, although looking beyond the name is important too as you can’t always count on the manufacturers. Ideally, find something specifically for container plants that’s peat or coir based and feels more fluffy and light than heavy - if you look at NECM's pictures you can see all the air space in the mix wear it can breath and get oxygen to the roots. Avoid topsoil as an ingredient at all costs. Within reason, a slightly more expensive higher quality mix makes a difference.
That’s my 2 cents anyway.