Is there a pull of skilled workforce from rural to urban areas? Is there a pull of skilled workforce from rural to urban areas, i.e. is this scientifically described?

Especially in the European Union.
It somewhat depends what you mean by that. The process is more complicated with migrants to cities also acquiring skills/education there, e.g.


  Another important piece of work related to education-based motivation is Lucas (2004), who constructs a two-sector model where the urban sector pays a higher wage due to its high-skilled jobs which are not available to rural workers. Unskilled rural agents migrate to cities to accumulate human capital and invest in skills. Households’ preferences are isoelastic and they supply one unit of time endowment to either work or invest in human capital. Rural production uses labor and land; it has diminishing returns because land is fixed in quantity. The urban production technology is linear and requires only skilled labor input. Human capital investment can only take place in cities and labor is free to move between sectors. Rural–urban migration takes place once and for all with the growth rate of production of the urban (rural) sector changes from zero (one) to a constant positive level (zero). 


This is somewhat of a no-brainer, you don't expect PhDs in AI to just pop up in rural areas and then migrate to cities...

There's a monster EU document (some 350 pages) published in 2018 on migration patterns inside the Union.  As far as I can tell from that (its summary is poor), already [mostly the younger] skilled workers prefer to move to another EU country (with better wages, less corruption, etc.)

For healthcare workers, which the EU study spends a lot of time on, within a given EU country, there's indeed a more acute shortage in the rural areas (p. 266). However across EU countries healthcare workers may migrate from an urban area e.g. in Greece to a rural area in the UK, all because of pay, prospects etc. (p. 269)