Hi
Hopefully, it's not the old TDI disease with the gradually loosening KW (Krieger) timing belt tensioner

.
In some TDI systems, the initial amount seems to be a bit insufficient for some reason. If, then, the starter speed decreases over time (wear and tear / old battery), it takes longer and longer to start.
The 2-second warm-up time seems strange to me, especially during this time of year, and I haven't been able to find an explanation for it.